dimRed/0000755000176200001440000000000014153365332011463 5ustar liggesusersdimRed/NAMESPACE0000644000176200001440000000457414153217466012720 0ustar liggesusers# Generated by roxygen2: do not edit by hand export(AUC_lnK_R_NX) export(AutoEncoder) export(DRR) export(DiffusionMaps) export(DrL) export(FastICA) export(FruchtermanReingold) export(HLLE) export(Isomap) export(KamadaKawai) export(LCMC) export(LLE) export(LaplacianEigenmaps) export(MDS) export(NNMF) export(PCA) export(PCA_L1) export(Q_NX) export(Q_global) export(Q_local) export(R_NX) export(UMAP) export(dataSetList) export(dimRedData) export(dimRedMethodList) export(dimRedQualityList) export(dimRedResult) export(distance_correlation) export(embed) export(getRotationMatrix) export(installSuggests) export(inverse) export(kPCA) export(loadDataSet) export(mean_R_NX) export(mixColor1Ramps) export(mixColor2Ramps) export(mixColor3Ramps) export(mixColorRamps) export(nMDS) export(plot) export(plot_R_NX) export(predict) export(quality) export(reconstruction_error) export(reconstruction_rmse) export(tSNE) export(total_correlation) exportClasses(AutoEncoder) exportClasses(DRR) exportClasses(DiffusionMaps) exportClasses(DrL) exportClasses(FastICA) exportClasses(FruchtermanReingold) exportClasses(HLLE) exportClasses(Isomap) exportClasses(KamadaKawai) exportClasses(LLE) exportClasses(LaplacianEigenmaps) exportClasses(MDS) exportClasses(NNMF) exportClasses(PCA) exportClasses(PCA_L1) exportClasses(UMAP) exportClasses(dimRedData) exportClasses(dimRedMethod) exportClasses(dimRedResult) exportClasses(kPCA) exportClasses(nMDS) exportClasses(tSNE) exportMethods("[") exportMethods(AUC_lnK_R_NX) exportMethods(LCMC) exportMethods(Q_NX) exportMethods(Q_global) exportMethods(Q_local) exportMethods(R_NX) exportMethods(as.data.frame) exportMethods(as.dimRedData) exportMethods(cophenetic_correlation) exportMethods(distance_correlation) exportMethods(embed) exportMethods(getData) exportMethods(getDimRedData) exportMethods(getMeta) exportMethods(getNDim) exportMethods(getOrgData) exportMethods(getOtherData) exportMethods(getPars) exportMethods(inverse) exportMethods(maximize_correlation) exportMethods(mean_R_NX) exportMethods(ndims) exportMethods(nrow) exportMethods(plot) exportMethods(predict) exportMethods(print) exportMethods(quality) exportMethods(reconstruction_error) exportMethods(reconstruction_rmse) exportMethods(total_correlation) import(DRR) import(methods) import(utils) importFrom(grDevices,colorRamp) importFrom(grDevices,rgb) importFrom(graphics,plot) importFrom(magrittr,"%>%") importFrom(stats,predict) dimRed/LICENSE0000644000176200001440000007674512772463050012514 0ustar liggesusersGNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright © 2007 Free Software Foundation, Inc. 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If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee.dimRed/man/0000755000176200001440000000000013753034327012240 5ustar liggesusersdimRed/man/R_NX-dimRedResult-method.Rd0000644000176200001440000000244013753034327017214 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{R_NX,dimRedResult-method} \alias{R_NX,dimRedResult-method} \alias{R_NX} \title{Method R_NX} \usage{ \S4method{R_NX}{dimRedResult}(object, ndim = getNDim(object)) } \arguments{ \item{object}{of class dimRedResult} \item{ndim}{the number of dimensions to take from the embedded data.} } \description{ Calculate the R_NX score from Lee et. al. (2013) which shows the neighborhood preservation for the Kth nearest neighbors, corrected for random point distributions and scaled to range [0, 1]. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/Isomap-class.Rd0000644000176200001440000000571113753034327015066 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/isomap.R \docType{class} \name{Isomap-class} \alias{Isomap-class} \alias{Isomap} \title{Isomap embedding} \description{ An S4 Class implementing the Isomap Algorithm } \details{ The Isomap algorithm approximates a manifold using geodesic distances on a k nearest neighbor graph. Then classical scaling is performed on the resulting distance matrix. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ Isomap can take the following parameters: \describe{ \item{knn}{The number of nearest neighbors in the graph. Defaults to 50.} \item{ndim}{The number of embedding dimensions, defaults to 2.} \item{get_geod}{Should the geodesic distance matrix be kept, if \code{TRUE}, access it as \code{getOtherData(x)$geod}} } } \section{Implementation}{ The dimRed package uses its own implementation of Isomap which also comes with an out of sample extension (known as landmark Isomap). The default Isomap algorithm scales computationally not very well, the implementation here uses \code{\link[RANN]{nn2}} for a faster search of the nearest neighbors. If data are too large it may be useful to fit a subsample of the data and use the out-of-sample extension for the other points. } \examples{ dat <- loadDataSet("3D S Curve", n = 500) emb <- embed(dat, "Isomap", knn = 10) plot(emb) ## or simpler, use embed(): samp <- sample(nrow(dat), size = 200) emb2 <- embed(dat[samp], "Isomap", .mute = NULL, knn = 10) emb3 <- predict(emb2, dat[-samp]) plot(emb2, type = "2vars") plot(emb3, type = "2vars") } \references{ Tenenbaum, J.B., Silva, V. de, Langford, J.C., 2000. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290, 2319-2323. https://doi.org/10.1126/science.290.5500.2319 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/AutoEncoder-class.Rd0000644000176200001440000001246314153166463016052 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/autoencoder.R \docType{class} \name{AutoEncoder-class} \alias{AutoEncoder-class} \alias{AutoEncoder} \title{AutoEncoder} \description{ An S4 Class implementing an Autoencoder } \details{ Autoencoders are neural networks that try to reproduce their input. Consider this method unstable, as the internals may still be changed. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ Autoencoder can take the following parameters: \describe{ \item{ndim}{The number of dimensions for reduction.} \item{n_hidden}{The number of neurons in the hidden layers, the length specifies the number of layers, the length must be impair, the middle number must be the same as ndim.} \item{activation}{The activation functions for the layers, one of "tanh", "sigmoid", "relu", "elu", everything else will silently be ignored and there will be no activation function for the layer.} \item{weight_decay}{the coefficient for weight decay, set to 0 if no weight decay desired.} \item{learning_rate}{The learning rate for gradient descend} \item{graph}{Optional: A list of bits and pieces that define the autoencoder in tensorflow, see details.} \item{keras_graph}{Optional: A list of keras layers that define the encoder and decoder, specifying this, will ignore all other topology related variables, see details.} \item{batchsize}{If NA, all data will be used for training, else only a random subset of size batchsize will be used} \item{n_steps}{the number of training steps.} } } \section{Details}{ There are several ways to specify an autoencoder, the simplest is to pass the number of neurons per layer in \code{n_hidden}, this must be a vector of integers of impair length and it must be symmetric and the middle number must be equal to \code{ndim}, For every layer an activation function can be specified with \code{activation}. For regularization weight decay can be specified by setting \code{weight_decay} > 0. Currently only a gradient descent optimizer is used, the learning rate can be specified by setting \code{learning_rate}. The learner can operate on batches if \code{batchsize} is not \code{NA}. The number of steps the learner uses is specified using \code{n_steps}. } \section{Further training a model}{ If the model did not converge in the first training phase or training with different data is desired, the \code{\link{dimRedResult}} object may be passed as \code{autoencoder} parameter; In this case all topology related parameters will be ignored. } \section{Using Keras layers}{ The encoder and decoder part can be specified using a list of \pkg{keras} layers. This requires a list with two entries, \code{encoder} should contain a LIST of keras layers WITHOUT the \code{\link[keras]{layer_input}} that will be concatenated in order to form the encoder part. \code{decoder} should be defined accordingly, the output of \code{decoder} must have the same number of dimensions as the input data. } \section{Using Tensorflow}{ The model can be entirely defined in \pkg{tensorflow}, it must contain a list with the following entries: \describe{ \item{encoder}{A tensor that defines the encoder.} \item{decoder}{A tensor that defines the decoder.} \item{network}{A tensor that defines the reconstruction (encoder + decoder).} \item{loss}{A tensor that calculates the loss (network + loss function).} \item{in_data}{A \code{placeholder} that points to the data input of the network AND the encoder.} \item{in_decoder}{A \code{placeholder} that points to the input of the decoder.} \item{session}{A \pkg{tensorflow} \code{Session} object that holds the values of the tensors.} } } \section{Implementation}{ Uses \pkg{tensorflow} as a backend, for details an problems relating tensorflow, see \url{https://tensorflow.rstudio.com}. } \examples{ \dontrun{ dat <- loadDataSet("3D S Curve") emb <- embed(dat, "AutoEncoder") # predicting is possible: samp <- sample(floor(nrow(dat) / 10)) emb2 <- embed(dat[samp]) emb3 <- predict(emb2, dat[-samp]) plot(emb, type = "2vars") plot(emb2, type = "2vars") points(getData(emb3)) } } \seealso{ Other dimensionality reduction methods: \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/mixColorRamps.Rd0000644000176200001440000000241113753034327015324 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mixColorSpaces.R \name{mixColorRamps} \alias{mixColorRamps} \alias{mixColor1Ramps} \alias{mixColor2Ramps} \alias{mixColor3Ramps} \title{Mixing color ramps} \usage{ mixColorRamps(vars, ramps) mixColor1Ramps(vars, ramps = colorRamp(c("blue", "black", "red"))) mixColor2Ramps( vars, ramps = list(colorRamp(c("blue", "green")), colorRamp(c("blue", "red"))) ) mixColor3Ramps( vars, ramps = list(colorRamp(c("#001A00", "#00E600")), colorRamp(c("#00001A", "#0000E6")), colorRamp(c("#1A0000", "#E60000"))) ) } \arguments{ \item{vars}{a list of variables} \item{ramps}{a list of color ramps, one for each variable.} } \description{ mix different color ramps } \details{ automatically create colors to represent a varying number of dimensions. } \examples{ cols <- expand.grid(x = seq(0, 1, length.out = 10), y = seq(0, 1, length.out = 10), z = seq(0, 1, length.out = 10)) mixed <- mixColor3Ramps(cols) \dontrun{ library(rgl) plot3d(cols$x, cols$y, cols$z, col = mixed, pch = 15) cols <- expand.grid(x = seq(0, 1, length.out = 10), y = seq(0, 1, length.out = 10)) mixed <- mixColor2Ramps(cols) } plot(cols$x, cols$y, col = mixed, pch = 15) } dimRed/man/mean_R_NX-dimRedResult-method.Rd0000644000176200001440000000215113753034327020213 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{mean_R_NX,dimRedResult-method} \alias{mean_R_NX,dimRedResult-method} \alias{mean_R_NX} \title{Method mean_R_NX} \usage{ \S4method{mean_R_NX}{dimRedResult}(object) } \arguments{ \item{object}{of class dimRedResult} } \description{ Calculate the mean_R_NX score to assess the quality of a dimensionality reduction. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/getRotationMatrix.Rd0000644000176200001440000000152113371631672016214 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/get_info.R \name{getRotationMatrix} \alias{getRotationMatrix} \title{getRotationMatrix} \usage{ getRotationMatrix(x) } \arguments{ \item{x}{of type \code{\link{dimRedResult}}} } \value{ a matrix } \description{ Extract the rotation matrix from \code{\link{dimRedResult}} objects derived from PCA and FastICA } \details{ The data has to be pre-processed the same way as the method does, e.g. centering and/or scaling. } \examples{ dat <- loadDataSet("Iris") pca <- embed(dat, "PCA") ica <- embed(dat, "FastICA") rot_pca <- getRotationMatrix(pca) rot_ica <- getRotationMatrix(ica) scale(getData(dat), TRUE, FALSE) \%*\% rot_pca - getData(getDimRedData(pca)) scale(getData(dat), TRUE, FALSE) \%*\% rot_ica - getData(getDimRedData(ica)) } \concept{convenience functions} dimRed/man/distance_correlation-dimRedResult-method.Rd0000644000176200001440000000224513753034327022604 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{distance_correlation,dimRedResult-method} \alias{distance_correlation,dimRedResult-method} \alias{distance_correlation} \title{Method distance_correlation} \usage{ \S4method{distance_correlation}{dimRedResult}(object) } \arguments{ \item{object}{of class dimRedResult} } \description{ Calculate the distance correlation between the distance matrices in high and low dimensioal space. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/tSNE-class.Rd0000644000176200001440000000536613753034327014455 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tsne.R \docType{class} \name{tSNE-class} \alias{tSNE-class} \alias{tSNE} \title{t-Distributed Stochastic Neighborhood Embedding} \description{ An S4 Class for t-SNE. } \details{ t-SNE is a method that uses Kullback-Leibler divergence between the distance matrices in high and low-dimensional space to embed the data. The method is very well suited to visualize complex structures in low dimensions. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ t-SNE can take the following parameters: \describe{ \item{d}{A distance function, defaults to euclidean distances} \item{perplexity}{The perplexity parameter, roughly equivalent to neighborhood size.} \item{theta}{Approximation for the nearest neighbour search, large values are more inaccurate.} \item{ndim}{The number of embedding dimensions.} } } \section{Implementation}{ Wraps around \code{\link[Rtsne]{Rtsne}}, which is very well documented. Setting \code{theta = 0} does a normal t-SNE, larger values for \code{theta < 1} use the Barnes-Hut algorithm which scales much nicer with data size. Larger values for perplexity take larger neighborhoods into account. } \examples{ \dontrun{ dat <- loadDataSet("3D S Curve", n = 300) emb <- embed(dat, "tSNE", perplexity = 80) plot(emb, type = "2vars") } } \references{ Maaten, L. van der, 2014. Accelerating t-SNE using Tree-Based Algorithms. Journal of Machine Learning Research 15, 3221-3245. van der Maaten, L., Hinton, G., 2008. Visualizing Data using t-SNE. J. Mach. Learn. Res. 9, 2579-2605. } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}} } \concept{dimensionality reduction methods} dimRed/man/LCMC-dimRedResult-method.Rd0000644000176200001440000000221113753034327017120 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{LCMC,dimRedResult-method} \alias{LCMC,dimRedResult-method} \alias{LCMC} \title{Method LCMC} \usage{ \S4method{LCMC}{dimRedResult}(object) } \arguments{ \item{object}{of class dimRedResult} } \description{ Calculates the Local Continuity Meta Criterion, which is \code{\link{Q_NX}} adjusted for random overlap inside the K-ary neighborhood. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/getOtherData.Rd0000644000176200001440000000053013371631672015102 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getOtherData} \alias{getOtherData} \title{Method getOtherData} \usage{ getOtherData(object, ...) } \arguments{ \item{object}{The object to extract data from.} \item{...}{other arguments.} } \description{ Extract other data produced by a dimRedMethod } dimRed/man/DiffusionMaps-class.Rd0000644000176200001440000000641013753034327016402 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/diffmap.R \docType{class} \name{DiffusionMaps-class} \alias{DiffusionMaps-class} \alias{DiffusionMaps} \title{Diffusion Maps} \description{ An S4 Class implementing Diffusion Maps } \details{ Diffusion Maps uses a diffusion probability matrix to robustly approximate a manifold. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ Diffusion Maps can take the following parameters: \describe{ \item{d}{a function transforming a matrix row wise into a distance matrix or \code{dist} object, e.g. \code{\link[stats]{dist}}.} \item{ndim}{The number of dimensions} \item{eps}{The epsilon parameter that determines the diffusion weight matrix from a distance matrix \code{d}, \eqn{exp(-d^2/eps)}, if set to \code{"auto"} it will be set to the median distance to the 0.01*n nearest neighbor.} \item{t}{Time-scale parameter. The recommended value, 0, uses multiscale geometry.} \item{delta}{Sparsity cut-off for the symmetric graph Laplacian, a higher value results in more sparsity and faster calculation. The predefined value is 10^-5.} } } \section{Implementation}{ Wraps around \code{\link[diffusionMap]{diffuse}}, see there for details. It uses the notation of Richards et al. (2009) which is slightly different from the one in the original paper (Coifman and Lafon, 2006) and there is no \eqn{\alpha} parameter. There is also an out-of-sample extension, see examples. } \examples{ dat <- loadDataSet("3D S Curve", n = 300) emb <- embed(dat, "DiffusionMaps") plot(emb, type = "2vars") # predicting is possible: samp <- sample(floor(nrow(dat) / 10)) emb2 <- embed(dat[samp]) emb3 <- predict(emb2, dat[-samp]) plot(emb2, type = "2vars") points(getData(emb3)) } \references{ Richards, J.W., Freeman, P.E., Lee, A.B., Schafer, C.M., 2009. Exploiting Low-Dimensional Structure in Astronomical Spectra. ApJ 691, 32. doi:10.1088/0004-637X/691/1/32 Coifman, R.R., Lafon, S., 2006. Diffusion maps. Applied and Computational Harmonic Analysis 21, 5-30. doi:10.1016/j.acha.2006.04.006 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/maximize_correlation-dimRedResult-method.Rd0000644000176200001440000000175713753034327022644 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/rotate.R \name{maximize_correlation,dimRedResult-method} \alias{maximize_correlation,dimRedResult-method} \alias{maximize_correlation} \title{Maximize Correlation with the Axes} \usage{ \S4method{maximize_correlation}{dimRedResult}( object, naxes = ncol(object@data@data), cor_method = "pearson" ) } \arguments{ \item{object}{A dimRedResult object} \item{naxes}{the number of axes to optimize for.} \item{cor_method}{which correlation method to use} } \description{ Rotates the data in such a way that the correlation with the first \code{naxes} axes is maximized. } \details{ Methods that do not use eigenvector decomposition, like t-SNE often do not align the data with axes according to the correlation of variables with the data. \code{maximize_correlation} uses the \code{\link[optimx]{optimx}} package to rotate the data in such a way that the original variables have maximum correlation with the embedding axes. } dimRed/man/dimRedMethod-class.Rd0000644000176200001440000000340713753034327016203 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dimRedMethod-class.R \docType{class} \name{dimRedMethod-class} \alias{dimRedMethod-class} \title{Class "dimRedMethod"} \description{ A virtual class "dimRedMethod" to serve as a template to implement methods for dimensionality reduction. } \details{ Implementations of dimensionality reductions should inherit from this class. The \code{fun} slot should be a function that takes three arguments \describe{ \item{data}{An object of class \code{\link{dimRedData}}.} \item{pars}{A list with the standard parameters.} \item{keep.org.data}{Logical. If the original data should be kept in the output.} } and returns an object of class \code{\link{dimRedResult}}. The \code{stdpars} slot should take a list that contains standard parameters for the implemented methods. This way the method can be called by \code{embed(data, "method-name", ...)}, where \code{...} can be used to to change single parameters. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding.} \item{\code{stdpars}}{A list with the default parameters for the \code{fun} slot.} }} \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/kPCA-class.Rd0000644000176200001440000000501413753034327014410 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/kpca.R \docType{class} \name{kPCA-class} \alias{kPCA-class} \alias{kPCA} \title{Kernel PCA} \description{ An S4 Class implementing Kernel PCA } \details{ Kernel PCA is a nonlinear extension of PCA using kernel methods. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ Kernel PCA can take the following parameters: \describe{ \item{ndim}{the number of output dimensions, defaults to 2} \item{kernel}{The kernel function, either as a function or a character vector with the name of the kernel. Defaults to \code{"rbfdot"}} \item{kpar}{A list with the parameters for the kernel function, defaults to \code{list(sigma = 0.1)}} } The most comprehensive collection of kernel functions can be found in \code{\link[kernlab]{kpca}}. In case the function does not take any parameters \code{kpar} has to be an empty list. } \section{Implementation}{ Wraps around \code{\link[kernlab]{kpca}}, but provides additionally forward and backward projections. } \examples{ \dontrun{ dat <- loadDataSet("3D S Curve") emb <- embed(dat, "kPCA") plot(emb, type = "2vars") } } \references{ Sch\"olkopf, B., Smola, A., M\"uller, K.-R., 1998. Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299-1319. https://doi.org/10.1162/089976698300017467 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/dimRedData-class.Rd0000644000176200001440000000602513753034327015633 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dimRedData-class.R \docType{class} \name{dimRedData-class} \alias{dimRedData-class} \alias{dimRedData} \alias{as.data.frame,dimRedData-method} \alias{getData,dimRedData-method} \alias{getMeta,dimRedData-method} \alias{nrow,dimRedData-method} \alias{[,dimRedData,ANY,ANY,ANY-method} \alias{ndims,dimRedData-method} \title{Class "dimRedData"} \usage{ \S4method{as.data.frame}{dimRedData}(x, meta.prefix = "meta.", data.prefix = "") \S4method{getData}{dimRedData}(object) \S4method{getMeta}{dimRedData}(object) \S4method{nrow}{dimRedData}(x) \S4method{[}{dimRedData,ANY,ANY,ANY}(x, i) \S4method{ndims}{dimRedData}(object) } \arguments{ \item{x}{Of class dimRedData} \item{meta.prefix}{Prefix for the columns of the meta data names.} \item{data.prefix}{Prefix for the columns of the variable names.} \item{object}{Of class dimRedData.} \item{i}{a valid index for subsetting rows.} } \description{ A class to hold data for dimensionality reduction and methods. } \details{ The class hast two slots, \code{data} and \code{meta}. The \code{data} slot contains a \code{numeric matrix} with variables in columns and observations in rows. The \code{meta} slot may contain a \code{data.frame} with additional information. Both slots need to have the same number of rows or the \code{meta} slot needs to contain an empty \code{data.frame}. See examples for easy conversion from and to \code{data.frame}. For plotting functions see \code{\link{plot.dimRedData}}. } \section{Methods (by generic)}{ \itemize{ \item \code{as.data.frame}: convert to data.frame \item \code{getData}: Get the data slot. \item \code{getMeta}: Get the meta slot. \item \code{nrow}: Get the number of observations. \item \code{[}: Subset rows. \item \code{ndims}: Extract the number of Variables from the data. }} \section{Slots}{ \describe{ \item{\code{data}}{of class \code{matrix}, holds the data, observations in rows, variables in columns} \item{\code{meta}}{of class \code{data.frame}, holds meta data such as classes, internal manifold coordinates, or simply additional data of the data set. Must have the same number of rows as the \code{data} slot or be an empty data frame.} }} \examples{ ## Load an example data set: s3d <- loadDataSet("3D S Curve") ## Create using a constructor: ### without meta information: dimRedData(iris[, 1:4]) ### with meta information: dimRedData(iris[, 1:4], iris[, 5]) ### using slot names: dimRedData(data = iris[, 1:4], meta = iris[, 5]) ## Convert to a dimRedData objects: Iris <- as(iris[, 1:4], "dimRedData") ## Convert to data.frame: head(as(s3d, "data.frame")) head(as.data.frame(s3d)) head(as.data.frame(as(iris[, 1:4], "dimRedData"))) ## Extract slots: head(getData(s3d)) head(getMeta(s3d)) ## Get the number of observations: nrow(s3d) ## Subset: s3d[1:5, ] ## Shuffle data: s3 <- s3d[nrow(s3d)] ## Get the number of variables: ndims(s3d) } \seealso{ Other dimRedData: \code{\link{as.dimRedData}()} Other dimRedData: \code{\link{as.dimRedData}()} } \concept{dimRedData} dimRed/man/dataSets.Rd0000644000176200001440000000253413065033470014275 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dataSets.R \name{dataSets} \alias{dataSets} \alias{loadDataSet} \alias{dataSetList} \title{Example Data Sets for dimensionality reduction} \usage{ loadDataSet(name = dataSetList(), n = 2000, sigma = 0.05) dataSetList() } \arguments{ \item{name}{A character vector that specifies the name of the data set.} \item{n}{In generated data sets the number of points to be generated, else ignored.} \item{sigma}{In generated data sets the standard deviation of the noise added, else ignored.} } \value{ \code{loadDataSet} an object of class \code{\link{dimRedData}}. \code{dataSetList()} return a character string with the implemented data sets } \description{ A compilation of standard data sets that are often being used to showcase dimensionality reduction techniques. } \details{ The argument \code{name} should be one of \code{dataSetList()}. Partial matching is possible, see \code{\link{match.arg}}. Generated data sets contain the internal coordinates of the manifold in the \code{meta} slot. Call \code{dataSetList()} to see what data sets are available. } \examples{ ## a list of available data sets: dataSetList() ## Load a data set: swissRoll <- loadDataSet("Swiss Roll") \donttest{plot(swissRoll, type = "3vars")} ## Load Iris data set, partial matching: loadDataSet("I") } dimRed/man/Q_global-dimRedResult-method.Rd0000644000176200001440000000214413753034327020127 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{Q_global,dimRedResult-method} \alias{Q_global,dimRedResult-method} \alias{Q_global} \title{Method Q_global} \usage{ \S4method{Q_global}{dimRedResult}(object) } \arguments{ \item{object}{of class dimRedResult} } \description{ Calculate the Q_global score to assess the quality of a dimensionality reduction. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/installSuggests.Rd0000644000176200001440000000112513065033470015713 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{installSuggests} \alias{installSuggests} \title{getSuggests} \usage{ installSuggests() } \description{ Install packages wich are suggested by dimRed. } \details{ By default dimRed will not install all the dependencies, because there are quite a lot and in case some of them are not available for your platform you will not be able to install dimRed without problems. To solve this I provide a function which automatically installes all the suggested packages. } \examples{ \dontrun{ installSuggests() } } dimRed/man/cophenetic_correlation-dimRedResult-method.Rd0000644000176200001440000000244213753034327023132 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{cophenetic_correlation,dimRedResult-method} \alias{cophenetic_correlation,dimRedResult-method} \alias{cophenetic_correlation} \title{Method cophenetic_correlation} \usage{ \S4method{cophenetic_correlation}{dimRedResult}(object, d = stats::dist, cor_method = "pearson") } \arguments{ \item{object}{of class dimRedResult} \item{d}{the distance function to use.} \item{cor_method}{The correlation method.} } \description{ Calculate the correlation between the distance matrices in high and low dimensioal space. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/LaplacianEigenmaps-class.Rd0000644000176200001440000000415013562225201017336 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/leim.R \docType{class} \name{LaplacianEigenmaps-class} \alias{LaplacianEigenmaps-class} \alias{LaplacianEigenmaps} \title{Laplacian Eigenmaps} \description{ An S4 Class implementing Laplacian Eigenmaps } \details{ Laplacian Eigenmaps use a kernel and were originally developed to separate non-convex clusters under the name spectral clustering. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ \code{LaplacianEigenmaps} can take the following parameters: \describe{ \item{ndim}{the number of output dimensions.} \item{sparse}{A character vector specifying hot to make the graph sparse, \code{"knn"} means that a K-nearest neighbor graph is constructed, \code{"eps"} an epsilon neighborhood graph is constructed, else a dense distance matrix is used.} \item{knn}{The number of nearest neighbors to use for the knn graph.} \item{eps}{The distance for the epsilon neighborhood graph.} \item{t}{Parameter for the transformation of the distance matrix by \eqn{w=exp(-d^2/t)}, larger values give less weight to differences in distance, \code{t == Inf} treats all distances != 0 equally.} \item{norm}{logical, should the normed laplacian be used?} } } \section{Implementation}{ Wraps around \code{\link[loe]{spec.emb}}. } \examples{ dat <- loadDataSet("3D S Curve") emb <- embed(dat, "LaplacianEigenmaps") plot(emb@data@data) } \references{ Belkin, M., Niyogi, P., 2003. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation 15, 1373. } dimRed/man/getDimRedData.Rd0000644000176200001440000000050213065033470015154 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getDimRedData} \alias{getDimRedData} \title{Method getDimRedData} \usage{ getDimRedData(object, ...) } \arguments{ \item{object}{The object to extract data from.} \item{...}{other arguments.} } \description{ Extract dimRedData. } dimRed/man/total_correlation-dimRedResult-method.Rd0000644000176200001440000000263113753034327022134 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{total_correlation,dimRedResult-method} \alias{total_correlation,dimRedResult-method} \alias{total_correlation} \title{Method total_correlation} \usage{ \S4method{total_correlation}{dimRedResult}( object, naxes = ndims(object), cor_method = "pearson", is.rotated = FALSE ) } \arguments{ \item{object}{of class dimRedResult} \item{naxes}{the number of axes to use for optimization.} \item{cor_method}{the correlation method to use.} \item{is.rotated}{if FALSE the object is rotated.} } \description{ Calculate the total correlation of the variables with the axes to assess the quality of a dimensionality reduction. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/getNDim.Rd0000644000176200001440000000051013141064362014043 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getNDim} \alias{getNDim} \title{Method getNDim} \usage{ getNDim(object, ...) } \arguments{ \item{object}{The object to get the dimensions from.} \item{...}{other arguments.} } \description{ Extract the number of embedding dimensions. } dimRed/man/KamadaKawai-class.Rd0000644000176200001440000000561313753034327015772 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/graph_embed.R \docType{class} \name{KamadaKawai-class} \alias{KamadaKawai-class} \alias{KamadaKawai} \title{Graph Embedding via the Kamada Kawai Algorithm} \description{ An S4 Class implementing the Kamada Kawai Algorithm for graph embedding. } \details{ Graph embedding algorithms se the data as a graph. Between the nodes of the graph exist attracting and repelling forces which can be modeled as electrical fields or springs connecting the nodes. The graph is then forced into a lower dimensional representation that tries to represent the forces betweent he nodes accurately by minimizing the total energy of the attracting and repelling forces. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ KamadaKawai can take the following parameters: \describe{ \item{ndim}{The number of dimensions, defaults to 2. Can only be 2 or 3} \item{knn}{Reduce the graph to keep only the neares neighbors. Defaults to 100.} \item{d}{The distance function to determine the weights of the graph edges. Defaults to euclidean distances.} } } \section{Implementation}{ Wraps around \code{\link[igraph]{layout_with_kk}}. The parameters maxiter, epsilon and kkconst are set to the default values and cannot be set, this may change in a future release. The DimRed Package adds an extra sparsity parameter by constructing a knn graph which also may improve visualization quality. } \examples{ dat <- loadDataSet("Swiss Roll", n = 200) emb <- embed(dat, "KamadaKawai") plot(emb, type = "2vars") } \references{ Kamada, T., Kawai, S., 1989. An algorithm for drawing general undirected graphs. Information Processing Letters 31, 7-15. https://doi.org/10.1016/0020-0190(89)90102-6 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/PCA_L1-class.Rd0000644000176200001440000000543313753034327014576 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/l1pca.R \docType{class} \name{PCA_L1-class} \alias{PCA_L1-class} \alias{PCA_L1} \title{Principal Component Analysis with L1 error.} \description{ S4 Class implementing PCA with L1 error. } \details{ PCA transforms the data so that the L2 reconstruction error is minimized or the variance of the projected data is maximized. This is sensitive to outliers, L1 PCA minimizes the L1 reconstruction error or maximizes the sum of the L1 norm of the projected observations. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ PCA can take the following parameters: \describe{ \item{ndim}{The number of output dimensions.} \item{center}{logical, should the data be centered, defaults to \code{TRUE}.} \item{scale.}{logical, should the data be scaled, defaults to \code{FALSE}.} \item{fun}{character or function, the method to apply, see the \code{pcaL1} package} \item{\ldots}{other parameters for \code{fun}} } } \section{Implementation}{ Wraps around the different methods is the \code{pcaL1} package. Because PCA can be reduced to a simple rotation, forward and backward projection functions are supplied. } \examples{ if(requireNamespace("pcaL1", quietly = TRUE)) { dat <- loadDataSet("Iris") emb <- embed(dat, "PCA_L1") plot(emb, type = "2vars") plot(inverse(emb, getData(getDimRedData((emb)))), type = "3vars") } } \references{ Park, Y.W., Klabjan, D., 2016. Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis, in: Data Mining (ICDM), 2016 IEEE 16th International Conference On. IEEE, pp. 430-438. } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/LLE-class.Rd0000644000176200001440000000437613753034327014260 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/lle.R \docType{class} \name{LLE-class} \alias{LLE-class} \alias{LLE} \title{Locally Linear Embedding} \description{ An S4 Class implementing Locally Linear Embedding (LLE) } \details{ LLE approximates the points in the manifold by linear combination of its neighbors. These linear combinations are the same inside the manifold and in highdimensional space. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ LLE can take the following parameters: \describe{ \item{knn}{the number of neighbors for the knn graph., defaults to 50.} \item{ndim}{the number of embedding dimensions, defaults to 2.} } } \section{Implementation}{ Wraps around \code{\link[lle]{lle}}, only exposes the parameters \code{k} and \code{m}. } \examples{ dat <- loadDataSet("3D S Curve", n = 500) emb <- embed(dat, "LLE", knn = 45) plot(emb, type = "2vars") } \references{ Roweis, S.T., Saul, L.K., 2000. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290, 2323-2326. doi:10.1126/science.290.5500.2323 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/AUC_lnK_R_NX-dimRedResult-method.Rd0000644000176200001440000000347513753034327020521 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{AUC_lnK_R_NX,dimRedResult-method} \alias{AUC_lnK_R_NX,dimRedResult-method} \alias{AUC_lnK_R_NX} \title{Method AUC_lnK_R_NX} \usage{ \S4method{AUC_lnK_R_NX}{dimRedResult}(object, weight = "inv") } \arguments{ \item{object}{of class dimRedResult} \item{weight}{the weight function used, one of \code{c("inv", "log", "log10")}} } \description{ Calculate the Area under the R_NX(ln K), used in Lee et. al. (2015). Note that despite the name, this does not weight the mean by the logarithm, but by 1/K. If explicit weighting by the logarithm is desired use \code{weight = "log"} or \code{weight = "log10"} } \details{ The naming confusion originated from equation 17 in Lee et al (2015) and the name of this method may change in the future to avoid confusion. } \references{ Lee, J.A., Peluffo-Ordonez, D.H., Verleysen, M., 2015. Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure. Neurocomputing 169, 246-261. https://doi.org/10.1016/j.neucom.2014.12.095 } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/getPars.Rd0000644000176200001440000000045113065033470014126 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getPars} \alias{getPars} \title{Method getPars} \usage{ getPars(object, ...) } \arguments{ \item{object}{The object to be converted.} \item{...}{other arguments.} } \description{ Extracts the pars slot. } dimRed/man/quality.Rd0000644000176200001440000001101713753034327014217 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{quality,dimRedResult-method} \alias{quality,dimRedResult-method} \alias{quality} \alias{quality.dimRedResult} \alias{dimRedQualityList} \title{Quality Criteria for dimensionality reduction.} \usage{ \S4method{quality}{dimRedResult}(.data, .method = dimRedQualityList(), .mute = character(0), ...) dimRedQualityList() } \arguments{ \item{.data}{object of class \code{dimRedResult}} \item{.method}{character vector naming one of the methods} \item{.mute}{what output from the embedding method should be muted.} \item{...}{the pameters, internally passed as a list to the quality method as \code{pars = list(...)}} } \value{ a number } \description{ A collection of functions to compute quality measures on \code{\link{dimRedResult}} objects. } \section{Methods (by class)}{ \itemize{ \item \code{dimRedResult}: Calculate a quality index from a dimRedResult object. }} \section{Implemented methods}{ Method must be one of \code{"\link{Q_local}", "\link{Q_global}", "\link{mean_R_NX}", "\link{total_correlation}", "\link{cophenetic_correlation}", "\link{distance_correlation}", "\link{reconstruction_rmse}"} } \section{Rank based criteria}{ \code{Q_local}, \code{Q_global}, and \code{mean_R_NX} are quality criteria based on the Co-ranking matrix. \code{Q_local} and \code{Q_global} determine the local/global quality of the embedding, while \code{mean_R_NX} determines the quality of the overall embedding. They are parameter free and return a single number. The object must include the original data. The number returns is in the range [0, 1], higher values mean a better local/global embedding. } \section{Correlation based criteria}{ \code{total_correlation} calculates the sum of the mean squared correlations of the original axes with the axes in reduced dimensions, because some methods do not care about correlations with axes, there is an option to rotate data in reduced space to maximize this criterium. The number may be greater than one if more dimensions are summed up. \code{cophenetic_correlation} calculate the correlation between the lower triangles of distance matrices, the correlation and distance methods may be specified. The result is in range [-1, 1]. \code{distance_correlation} measures the independes of samples by calculating the correlation of distances. For details see \code{\link[energy]{dcor}}. } \section{Reconstruction error}{ \code{reconstruction_rmse} calculates the root mean squared error of the reconstrucion. \code{object} requires an inverse function. } \examples{ \dontrun{ embed_methods <- dimRedMethodList() quality_methods <- dimRedQualityList() scurve <- loadDataSet("Iris") quality_results <- matrix(NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods)) embedded_data <- list() for (e in embed_methods) { message("embedding: ", e) embedded_data[[e]] <- embed(scurve, e, .mute = c("message", "output")) for (q in quality_methods) { message(" quality: ", q) quality_results[e, q] <- tryCatch( quality(embedded_data[[e]], q), error = function (e) NA ) } } print(quality_results) } } \references{ Lueks, W., Mokbel, B., Biehl, M., Hammer, B., 2011. How to Evaluate Dimensionality Reduction? - Improving the Co-ranking Matrix. arXiv:1110.3917 [cs]. Szekely, G.J., Rizzo, M.L., Bakirov, N.K., 2007. Measuring and testing dependence by correlation of distances. Ann. Statist. 35, 2769-2794. doi:10.1214/009053607000000505 Lee, J.A., Peluffo-Ordonez, D.H., Verleysen, M., 2015. Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure. Neurocomputing, 169, 246-261. doi:10.1016/j.neucom.2014.12.095 } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \author{ Guido Kraemer } \concept{Quality scores for dimensionality reduction} dimRed/man/HLLE-class.Rd0000644000176200001440000000431313753034327014357 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hlle.R \docType{class} \name{HLLE-class} \alias{HLLE-class} \alias{HLLE} \title{Hessian Locally Linear Embedding} \description{ An S4 Class implementing Hessian Locally Linear Embedding (HLLE) } \details{ HLLE uses local hessians to approximate the curvines and is an extension to non-convex subsets in lowdimensional space. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ HLLE can take the following parameters: \describe{ \item{knn}{neighborhood size} \item{ndim}{number of output dimensions} } } \section{Implementation}{ Own implementation, sticks to the algorithm in Donoho and Grimes (2003). Makes use of sparsity to speed up final embedding. } \examples{ dat <- loadDataSet("3D S Curve", n = 300) emb <- embed(dat, "HLLE", knn = 15) plot(emb, type = "2vars") } \references{ Donoho, D.L., Grimes, C., 2003. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. PNAS 100, 5591-5596. doi:10.1073/pnas.1031596100 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/embed.Rd0000644000176200001440000000605313753034327013607 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/embed.R \name{embed} \alias{embed} \alias{embed,formula-method} \alias{embed,ANY-method} \alias{embed,dimRedData-method} \title{dispatches the different methods for dimensionality reduction} \usage{ embed(.data, ...) \S4method{embed}{formula}( .formula, .data, .method = dimRedMethodList(), .mute = character(0), .keep.org.data = TRUE, ... ) \S4method{embed}{ANY}( .data, .method = dimRedMethodList(), .mute = character(0), .keep.org.data = TRUE, ... ) \S4method{embed}{dimRedData}( .data, .method = dimRedMethodList(), .mute = character(0), .keep.org.data = TRUE, ... ) } \arguments{ \item{.data}{object of class \code{\link{dimRedData}}, will be converted to be of class \code{\link{dimRedData}} if necessary; see examples for details.} \item{...}{the parameters, internally passed as a list to the dimensionality reduction method as \code{pars = list(...)}} \item{.formula}{a formula, see \code{\link{as.dimRedData}}.} \item{.method}{character vector naming one of the dimensionality reduction techniques.} \item{.mute}{a character vector containing the elements you want to mute (\code{c("message", "output")}), defaults to \code{character(0)}.} \item{.keep.org.data}{\code{TRUE}/\code{FALSE} keep the original data.} } \value{ an object of class \code{\link{dimRedResult}} } \description{ wraps around all dimensionality reduction functions. } \details{ Method must be one of \code{\link{dimRedMethodList}()}, partial matching is performed. All parameters start with a dot, to avoid clashes with partial argument matching (see the R manual section 4.3.2), if there should ever occur any clashes in the arguments, call the function with all arguments named, e.g. \code{embed(.data = dat, .method = "mymethod", .d = "some parameter")}. } \section{Methods (by class)}{ \itemize{ \item \code{formula}: embed a data.frame using a formula. \item \code{ANY}: Embed anything as long as it can be coerced to \code{\link{dimRedData}}. \item \code{dimRedData}: Embed a dimRedData object }} \examples{ ## embed a data.frame using a formula: as.data.frame( embed(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, iris, "PCA") ) ## embed a data.frame and return a data.frame as.data.frame(embed(iris[, 1:4], "PCA")) ## embed a matrix and return a data.frame as.data.frame(embed(as.matrix(iris[, 1:4]), "PCA")) \dontrun{ ## embed dimRedData objects embed_methods <- dimRedMethodList() quality_methods <- dimRedQualityList() dataset <- loadDataSet("Iris") quality_results <- matrix(NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods)) embedded_data <- list() for (e in embed_methods) { message("embedding: ", e) embedded_data[[e]] <- embed(dataset, e, .mute = c("message", "output")) for (q in quality_methods) { message(" quality: ", q) quality_results[e, q] <- tryCatch( quality(embedded_data[[e]], q), error = function(e) NA ) } } print(quality_results) } } dimRed/man/UMAP-class.Rd0000644000176200001440000000650214153200601014360 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/umap.R \docType{class} \name{UMAP-class} \alias{UMAP-class} \alias{UMAP} \title{Umap embedding} \description{ An S4 Class implementing the UMAP algorithm } \details{ Uniform Manifold Approximation is a gradient descend based algorithm that gives results similar to t-SNE, but scales better with the number of points. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ UMAP can take the follwing parameters: \describe{ \item{ndim}{The number of embedding dimensions.} \item{knn}{The number of neighbors to be used.} \item{d}{The distance metric to use.} \item{method}{\code{"naive"} for an R implementation, \code{"python"} for the reference implementation.} } Other method parameters can also be passed, see \code{\link[umap]{umap.defaults}} for details. The ones above have been standardized for the use with \code{dimRed} and will get automatically translated for \code{\link[umap]{umap}}. } \section{Implementation}{ The dimRed package wraps the \code{\link[umap]{umap}} packages which provides an implementation in pure R and also a wrapper around the original python package \code{umap-learn} (https://github.com/lmcinnes/umap/). This requires \code{umap-learn} version 0.4 installed, at the time of writing, there is already \code{umap-learn} 0.5 but it is not supported by the R package \code{\link[umap]{umap}}. The \code{"naive"} implementation is a pure R implementation and considered experimental at the point of writing this, it is also much slower than the python implementation. The \code{"python"} implementation is the reference implementation used by McInees et. al. (2018). It requires the \code{\link[reticulate]{reticulate}} package for the interaction with python and the python package \code{umap-learn} installed (use \code{pip install umap-learn}). } \examples{ \dontrun{ dat <- loadDataSet("3D S Curve", n = 300) emb <- embed(dat, "UMAP", .mute = NULL, knn = 10) plot(emb, type = "2vars") } } \references{ McInnes, Leland, and John Healy. "UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction." https://arxiv.org/abs/1802.03426 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/reconstruction_error-dimRedResult-method.Rd0000644000176200001440000000406713753034327022707 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{reconstruction_error,dimRedResult-method} \alias{reconstruction_error,dimRedResult-method} \alias{reconstruction_error} \title{Method reconstruction_error} \usage{ \S4method{reconstruction_error}{dimRedResult}(object, n = seq_len(ndims(object)), error_fun = "rmse") } \arguments{ \item{object}{of class dimRedResult} \item{n}{a positive integer or vector of integers \code{<= ndims(object)}} \item{error_fun}{a function or string indicating an error function, if indication a function it must take to matrices of the same size and return a scalar.} } \value{ a vector of number with the same length as \code{n} with the } \description{ Calculate the error using only the first \code{n} dimensions of the embedded data. \code{error_fun} can either be one of \code{c("rmse", "mae")} to calculate the root mean square error or the mean absolute error respectively, or a function that takes to equally sized vectors as input and returns a single number as output. } \examples{ \dontrun{ ir <- loadDataSet("Iris") ir.drr <- embed(ir, "DRR", ndim = ndims(ir)) ir.pca <- embed(ir, "PCA", ndim = ndims(ir)) rmse <- data.frame( rmse_drr = reconstruction_error(ir.drr), rmse_pca = reconstruction_error(ir.pca) ) matplot(rmse, type = "l") plot(ir) plot(ir.drr) plot(ir.pca) } } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \author{ Guido Kraemer } \concept{Quality scores for dimensionality reduction} dimRed/man/DRR-class.Rd0000644000176200001440000001077413753034327014272 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/drr.R \docType{class} \name{DRR-class} \alias{DRR-class} \alias{DRR} \title{Dimensionality Reduction via Regression} \description{ An S4 Class implementing Dimensionality Reduction via Regression (DRR). } \details{ DRR is a non-linear extension of PCA that uses Kernel Ridge regression. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ DRR can take the following parameters: \describe{ \item{ndim}{The number of dimensions} \item{lambda}{The regularization parameter for the ridge regression.} \item{kernel}{The kernel to use for KRR, defaults to \code{"rbfdot"}.} \item{kernel.pars}{A list with kernel parameters, elements depend on the kernel used, \code{"rbfdot"} uses \code{"sigma"}.} \item{pca}{logical, should an initial pca step be performed, defaults to \code{TRUE}.} \item{pca.center}{logical, should the data be centered before the pca step. Defaults to \code{TRUE}.} \item{pca.scale}{logical, should the data be scaled before the pca ste. Defaults to \code{FALSE}.} \item{fastcv}{logical, should \code{\link[CVST]{fastCV}} from the CVST package be used instead of normal cross-validation.} \item{fastcv.test}{If \code{fastcv = TRUE}, separate test data set for fastcv.} \item{cv.folds}{if \code{fastcv = FALSE}, specifies the number of folds for crossvalidation.} \item{fastkrr.nblocks}{integer, higher values sacrifice numerical accuracy for speed and less memory, see below for details.} \item{verbose}{logical, should the cross-validation results be printed out.} } } \section{Implementation}{ Wraps around \code{\link[DRR]{drr}}, see there for details. DRR is a non-linear extension of principal components analysis using Kernel Ridge Regression (KRR, details see \code{\link[CVST]{constructKRRLearner}} and \code{\link[DRR]{constructFastKRRLearner}}). Non-linear regression is used to explain more variance than PCA. DRR provides an out-of-sample extension and a backward projection. The most expensive computations are matrix inversions therefore the implementation profits a lot from a multithreaded BLAS library. The best parameters for each KRR are determined by cross-validaton over all parameter combinations of \code{lambda} and \code{kernel.pars}, using less parameter values will speed up computation time. Calculation of KRR can be accelerated by increasing \code{fastkrr.nblocks}, it should be smaller than n^{1/3} up to sacrificing some accuracy, for details see \code{\link[DRR]{constructFastKRRLearner}}. Another way to speed up is to use \code{pars$fastcv = TRUE} which might provide a more efficient way to search the parameter space but may also miss the global maximum, I have not ran tests on the accuracy of this method. } \examples{ \dontrun{ dat <- loadDataSet("variable Noise Helix", n = 200)[sample(200)] emb <- embed(dat, "DRR", ndim = 3) plot(dat, type = "3vars") plot(emb, type = "3vars") # We even have function to reconstruct, also working for only the first few dimensions rec <- inverse(emb, getData(getDimRedData(emb))[, 1, drop = FALSE]) plot(rec, type = "3vars") } } \references{ Laparra, V., Malo, J., Camps-Valls, G., 2015. Dimensionality Reduction via Regression in Hyperspectral Imagery. IEEE Journal of Selected Topics in Signal Processing 9, 1026-1036. doi:10.1109/JSTSP.2015.2417833 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/nMDS-class.Rd0000644000176200001440000000415413753034327014437 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nmds.R \docType{class} \name{nMDS-class} \alias{nMDS-class} \alias{nMDS} \title{Non-Metric Dimensional Scaling} \description{ An S4 Class implementing Non-Metric Dimensional Scaling. } \details{ A non-linear extension of MDS using monotonic regression } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ nMDS can take the following parameters: \describe{ \item{d}{A distance function.} \item{ndim}{The number of embedding dimensions.} } } \section{Implementation}{ Wraps around the \code{\link[vegan]{monoMDS}}. For parameters that are not available here, the standard configuration is used. } \examples{ dat <- loadDataSet("3D S Curve", n = 300) emb <- embed(dat, "nMDS") plot(emb, type = "2vars") } \references{ Kruskal, J.B., 1964. Nonmetric multidimensional scaling: A numerical method. Psychometrika 29, 115-129. https://doi.org/10.1007/BF02289694 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/PCA-class.Rd0000644000176200001440000000515513753034327014243 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/pca.R \docType{class} \name{PCA-class} \alias{PCA-class} \alias{PCA} \title{Principal Component Analysis} \description{ S4 Class implementing PCA. } \details{ PCA transforms the data in orthogonal components so that the first axis accounts for the larges variance in the data, all the following axes account for the highest variance under the constraint that they are orthogonal to the preceding axes. PCA is sensitive to the scaling of the variables. PCA is by far the fastest and simples method of dimensionality reduction and should probably always be applied as a baseline if other methods are tested. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ PCA can take the following parameters: \describe{ \item{ndim}{The number of output dimensions.} \item{center}{logical, should the data be centered, defaults to \code{TRUE}.} \item{scale.}{logical, should the data be scaled, defaults to \code{FALSE}.} } } \section{Implementation}{ Wraps around \code{\link{prcomp}}. Because PCA can be reduced to a simple rotation, forward and backward projection functions are supplied. } \examples{ dat <- loadDataSet("Iris") emb <- embed(dat, "PCA") plot(emb, type = "2vars") plot(inverse(emb, getDimRedData(emb)), type = "3vars") } \references{ Pearson, K., 1901. On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2, 559-572. } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/dimRedResult-class.Rd0000644000176200001440000000760013753034327016240 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dimRedResult-class.R \docType{class} \name{dimRedResult-class} \alias{dimRedResult-class} \alias{dimRedResult} \alias{predict,dimRedResult-method} \alias{inverse,dimRedResult-method} \alias{inverse} \alias{as.data.frame,dimRedResult-method} \alias{getPars,dimRedResult-method} \alias{getNDim,dimRedResult-method} \alias{print,dimRedResult-method} \alias{getOrgData,dimRedResult-method} \alias{getDimRedData,dimRedResult-method} \alias{ndims,dimRedResult-method} \alias{getOtherData,dimRedResult-method} \title{Class "dimRedResult"} \usage{ \S4method{predict}{dimRedResult}(object, xnew) \S4method{inverse}{dimRedResult}(object, ynew) \S4method{as.data.frame}{dimRedResult}( x, org.data.prefix = "org.", meta.prefix = "meta.", data.prefix = "" ) \S4method{getPars}{dimRedResult}(object) \S4method{getNDim}{dimRedResult}(object) \S4method{print}{dimRedResult}(x) \S4method{getOrgData}{dimRedResult}(object) \S4method{getDimRedData}{dimRedResult}(object) \S4method{ndims}{dimRedResult}(object) \S4method{getOtherData}{dimRedResult}(object) } \arguments{ \item{object}{Of class \code{dimRedResult}} \item{xnew}{new data, of type \code{\link{dimRedData}}} \item{ynew}{embedded data, of type \code{\link{dimRedData}}} \item{x}{Of class \code{dimRedResult}} \item{org.data.prefix}{Prefix for the columns of the org.data slot.} \item{meta.prefix}{Prefix for the columns of \code{x@data@meta}.} \item{data.prefix}{Prefix for the columns of \code{x@data@data}.} } \description{ A class to hold the results of of a dimensionality reduction. } \section{Methods (by generic)}{ \itemize{ \item \code{predict}: apply a trained method to new data, does not work with all methods, will give an error if there is no \code{apply}. In some cases the apply function may only be an approximation. \item \code{inverse}: inverse transformation of embedded data, does not work with all methods, will give an error if there is no \code{inverse}. In some cases the apply function may only be an approximation. \item \code{as.data.frame}: convert to \code{data.frame} \item \code{getPars}: Get the parameters with which the method was called. \item \code{getNDim}: Get the number of embedding dimensions. \item \code{print}: Method for printing. \item \code{getOrgData}: Get the original data and meta.data \item \code{getDimRedData}: Get the embedded data \item \code{ndims}: Extract the number of embedding dimensions. \item \code{getOtherData}: Get other data produced by the method }} \section{Slots}{ \describe{ \item{\code{data}}{Output data of class dimRedData.} \item{\code{org.data}}{original data, a matrix.} \item{\code{apply}}{a function to apply the method to out-of-sampledata, may not exist.} \item{\code{inverse}}{a function to calculate the original coordinates from reduced space, may not exist.} \item{\code{has.org.data}}{logical, if the original data is included in the object.} \item{\code{has.apply}}{logical, if a forward method is exists.} \item{\code{has.inverse}}{logical if an inverse method exists.} \item{\code{method}}{saves the method used.} \item{\code{pars}}{saves the parameters used.} \item{\code{other.data}}{other data produced by the method, e.g. a distance matrix.} }} \examples{ ## Create object by embedding data iris.pca <- embed(loadDataSet("Iris"), "PCA") ## Convert the result to a data.frame head(as(iris.pca, "data.frame")) head(as.data.frame(iris.pca)) ## There are no nameclashes to avoid here: head(as.data.frame(iris.pca, org.data.prefix = "", meta.prefix = "", data.prefix = "")) ## Print it more or less nicely: print(iris.pca) ## Get the embedded data as a dimRedData object: getDimRedData(iris.pca) ## Get the original data including meta information: getOrgData(iris.pca) ## Get the number of variables: ndims(iris.pca) } \concept{dimRedResult} dimRed/man/ndims.Rd0000644000176200001440000000050613065033470013634 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{ndims} \alias{ndims} \title{Method ndims} \usage{ ndims(object, ...) } \arguments{ \item{object}{To extract the number of dimensions from.} \item{...}{Arguments for further methods} } \description{ Extract the number of dimensions. } dimRed/man/NNMF-class.Rd0000644000176200001440000000544713753034327014402 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/nnmf.R \docType{class} \name{NNMF-class} \alias{NNMF-class} \alias{NNMF} \title{Non-Negative Matrix Factorization} \description{ S4 Class implementing NNMF. } \details{ NNMF is a method for decomposing a matrix into a smaller dimension such that the constraint that the data (and the projection) are not negative is taken into account. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ The method can take the following parameters: \describe{ \item{ndim}{The number of output dimensions.} \item{method}{character, which algorithm should be used. See \code{\link[NMF]{nmf}} for possible values. Defaults to "brunet"} \item{nrun}{integer, the number of times the computations are conducted. See \code{\link[NMF]{nmf}}} \item{seed}{integer, a value to control the random numbers used.} \item{options}{named list, other options to pass to \code{\link[NMF]{nmf}}} } } \section{Implementation}{ Wraps around \code{\link[NMF]{nmf}}. Note that the estimation uses random numbers. To create reproducible results, set the random number seed in the function call. Also, in many cases, the computations will be conducted in parallel using multiple cores. To disable this, use the option \code{.pbackend = NULL}. } \examples{ set.seed(4646) dat <- loadDataSet("Iris") emb <- embed(dat, "NNMF") plot(emb) # project new values: nn_proj <- predict(emb, dat[1:7]) plot(nn_proj) } \references{ Lee, D.D., Seung, H.S., 1999. Learning the parts of objects by non-negative matrix factorization. Nature 401, 788-791. https://doi.org/10.1038/44565 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/Q_NX-dimRedResult-method.Rd0000644000176200001440000000231113753034327017210 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{Q_NX,dimRedResult-method} \alias{Q_NX,dimRedResult-method} \alias{Q_NX} \title{Method Q_NX} \usage{ \S4method{Q_NX}{dimRedResult}(object) } \arguments{ \item{object}{of class dimRedResult} } \description{ Calculate the Q_NX score (Chen & Buja 2006, the notation in the publication is M_k). Which is the fraction of points that remain inside the same K-ary neighborhood in high and low dimensional space. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/Q_local-dimRedResult-method.Rd0000644000176200001440000000230713753034327017762 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{Q_local,dimRedResult-method} \alias{Q_local,dimRedResult-method} \alias{Q_local} \title{Method Q_local} \usage{ \S4method{Q_local}{dimRedResult}(object, ndim = getNDim(object)) } \arguments{ \item{object}{of class dimRedResult.} \item{ndim}{use the first ndim columns of the embedded data for calculation.} } \description{ Calculate the Q_local score to assess the quality of a dimensionality reduction. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/dimRedMethodList.Rd0000644000176200001440000000222513753034327015731 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dimRedMethod-class.R \name{dimRedMethodList} \alias{dimRedMethodList} \title{dimRedMethodList} \usage{ dimRedMethodList() } \value{ a character vector with the names of classes that inherit from \code{dimRedMethod}. } \description{ Get the names of all methods for dimensionality reduction. } \details{ Returns the name of all classes that inherit from \code{\link{dimRedMethod-class}} to use with \code{\link{embed}}. } \examples{ dimRedMethodList() } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/getData.Rd0000644000176200001440000000040613065033470014072 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getData} \alias{getData} \title{Method getData} \usage{ getData(object) } \arguments{ \item{object}{The object to be converted.} } \description{ Extracts the data slot. } dimRed/man/getMeta.Rd0000644000176200001440000000045113065033470014107 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getMeta} \alias{getMeta} \title{Method getMeta} \usage{ getMeta(object, ...) } \arguments{ \item{object}{The object to be converted.} \item{...}{other arguments.} } \description{ Extracts the meta slot. } dimRed/man/MDS-class.Rd0000644000176200001440000000511313753034327014255 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mds.R \docType{class} \name{MDS-class} \alias{MDS-class} \alias{MDS} \title{Metric Dimensional Scaling} \description{ An S4 Class implementing classical scaling (MDS). } \details{ MDS tries to maintain distances in high- and low-dimensional space, it has the advantage over PCA that arbitrary distance functions can be used, but it is computationally more demanding. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ MDS can take the following parameters: \describe{ \item{ndim}{The number of dimensions.} \item{d}{The function to calculate the distance matrix from the input coordinates, defaults to euclidean distances.} } } \section{Implementation}{ Wraps around \code{\link[stats]{cmdscale}}. The implementation also provides an out-of-sample extension which is not completely optimized yet. } \examples{ \dontrun{ dat <- loadDataSet("3D S Curve") emb <- embed(dat, "MDS") plot(emb, type = "2vars") # a "manual" kPCA: emb2 <- embed(dat, "MDS", d = function(x) exp(stats::dist(x))) plot(emb2, type = "2vars") # a "manual", more customizable, and slower Isomap: emb3 <- embed(dat, "MDS", d = function(x) vegan::isomapdist(vegan::vegdist(x, "manhattan"), k = 20)) plot(emb3) } } \references{ Torgerson, W.S., 1952. Multidimensional scaling: I. Theory and method. Psychometrika 17, 401-419. https://doi.org/10.1007/BF02288916 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/dimRed-package.Rd0000644000176200001440000000275714153177013015332 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dimRed.R \docType{package} \name{dimRed-package} \alias{dimRed} \alias{dimRed-package} \title{The dimRed package} \description{ This package simplifies dimensionality reduction in R by providing a framework of S4 classes and methods. dimRed collects dimensionality reduction methods that are implemented in R and implements others. It gives them a common interface and provides plotting functions for visualization and functions for quality assessment. Funding provided by the Department for Biogeochemical Integration, Empirical Inference of the Earth System Group, at the Max Plack Institute for Biogeochemistry, Jena. } \references{ Lee, J.A., Renard, E., Bernard, G., Dupont, P., Verleysen, M., 2013. Type 1 and 2 mixtures of Kullback-Leibler divergences as cost functions in dimensionality reduction based on similarity preservation. Neurocomputing. 112, 92-107. doi:10.1016/j.neucom.2012.12.036 Lee, J.A., Lee, J.A., Verleysen, M., 2008. Rank-based quality assessment of nonlinear dimensionality reduction. Proceedings of ESANN 2008 49-54. Chen, L., Buja, A., 2006. Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Layout and Proximity Analysis. } \seealso{ Useful links: \itemize{ \item \url{https://www.guido-kraemer.com/software/dimred/} \item Report bugs at \url{https://github.com/gdkrmr/dimRed/issues} } } \author{ \strong{Maintainer}: Guido Kraemer \email{guido.kraemer@uni-leipzig.de} } dimRed/man/makeKNNgraph.Rd0000644000176200001440000000141513065033470015030 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{makeKNNgraph} \alias{makeKNNgraph} \title{makeKNNgraph} \usage{ makeKNNgraph(x, k, eps = 0, diag = FALSE) } \arguments{ \item{x}{data, a matrix, observations in rows, dimensions in columns} \item{k}{the number of nearest neighbors.} \item{eps}{number, if \code{eps > 0} the KNN search is approximate, see \code{\link[RANN]{nn2}}} \item{diag}{logical, if \code{TRUE} every edge of the returned graph will have an edge with weight \code{0} to itself.} } \value{ an object of type \code{\link[igraph]{igraph}} with edge weight being the distances. } \description{ Create a K-nearest neighbor graph from data x. Uses \code{\link[RANN]{nn2}} as a fast way to find the neares neighbors. } dimRed/man/getOrgData.Rd0000644000176200001440000000047513065033470014550 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{getOrgData} \alias{getOrgData} \title{Method getOrgData} \usage{ getOrgData(object, ...) } \arguments{ \item{object}{The object to extract data from.} \item{...}{other arguments.} } \description{ Extract the Original data. } dimRed/man/as.dimRedData.Rd0000644000176200001440000000174613753034327015137 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R, R/dimRedData-class.R \name{as.dimRedData} \alias{as.dimRedData} \alias{as.dimRedData,formula-method} \title{Converts to dimRedData} \usage{ as.dimRedData(formula, ...) \S4method{as.dimRedData}{formula}(formula, data) } \arguments{ \item{formula}{The formula, left hand side is assigned to the meta slot right hand side is assigned to the data slot.} \item{...}{other arguments.} \item{data}{Will be coerced into a \code{\link{data.frame}} with \code{\link{as.data.frame}}} } \description{ Conversion functions to dimRedData. } \section{Methods (by class)}{ \itemize{ \item \code{formula}: Convert a \code{data.frame} to a dimRedData object using a formula }} \examples{ ## create a dimRedData object using a formula as.dimRedData(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, iris)[1:5] } \seealso{ Other dimRedData: \code{\link{dimRedData-class}} } \concept{dimRedData} dimRed/man/DrL-class.Rd0000644000176200001440000000504113753034327014313 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/graph_embed.R \docType{class} \name{DrL-class} \alias{DrL-class} \alias{DrL} \title{Distributed Recursive Graph Layout} \description{ An S4 Class implementing Distributed recursive Graph Layout. } \details{ DrL uses a complex algorithm to avoid local minima in the graph embedding which uses several steps. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ DrL can take the following parameters: \describe{ \item{ndim}{The number of dimensions, defaults to 2. Can only be 2 or 3} \item{knn}{Reduce the graph to keep only the neares neighbors. Defaults to 100.} \item{d}{The distance function to determine the weights of the graph edges. Defaults to euclidean distances.} } } \section{Implementation}{ Wraps around \code{\link[igraph]{layout_with_drl}}. The parameters maxiter, epsilon and kkconst are set to the default values and cannot be set, this may change in a future release. The DimRed Package adds an extra sparsity parameter by constructing a knn graph which also may improve visualization quality. } \examples{ \dontrun{ dat <- loadDataSet("Swiss Roll", n = 200) emb <- embed(dat, "DrL") plot(emb, type = "2vars") } } \references{ Martin, S., Brown, W.M., Wylie, B.N., 2007. Dr.l: Distributed Recursive (graph) Layout (No. dRl; 002182MLTPL00). Sandia National Laboratories. } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{FastICA-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/as.data.frame.Rd0000644000176200001440000000124213065033470015124 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{as.data.frame} \alias{as.data.frame} \title{Converts to data.frame} \usage{ as.data.frame(x, row.names, optional, ...) } \arguments{ \item{x}{The object to be converted} \item{row.names}{unused in \code{dimRed}} \item{optional}{unused in \code{dimRed}} \item{...}{other arguments.} } \description{ General conversions of objects created by \code{dimRed} to \code{data.frame}. See class documentations for details (\code{\link{dimRedData}}, \code{\link{dimRedResult}}). For the documentation of this function in base package, see here: \code{\link[base]{as.data.frame.default}}. } dimRed/man/plot.Rd0000644000176200001440000000370013753034327013505 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plot.R \name{plot} \alias{plot} \alias{plot.dimRed} \alias{plot,dimRedData,ANY-method} \alias{plot.dimRedData} \alias{plot,dimRedResult,ANY-method} \alias{plot.dimRedResult} \title{Plotting of dimRed* objects} \usage{ plot(x, y, ...) \S4method{plot}{dimRedData,ANY}( x, type = "pairs", vars = seq_len(ncol(x@data)), col = seq_len(min(3, ncol(x@meta))), ... ) \S4method{plot}{dimRedResult,ANY}( x, type = "pairs", vars = seq_len(ncol(x@data@data)), col = seq_len(min(3, ncol(x@data@meta))), ... ) } \arguments{ \item{x}{dimRedResult/dimRedData class, e.g. output of embedded/loadDataSet} \item{y}{Ignored} \item{...}{handed over to the underlying plotting function.} \item{type}{plot type, one of \code{c("pairs", "parpl", "2vars", "3vars", "3varsrgl")}} \item{vars}{the axes of the embedding to use for plotting} \item{col}{the columns of the meta slot to use for coloring, can be referenced as the column names or number of x@data} } \description{ Plots a object of class dimRedResult and dimRedData. For the documentation of the plotting function in base see here: \code{\link{plot.default}}. } \details{ Plotting functions for the classes usind in \code{dimRed}. they are intended to give a quick overview over the results, so they are somewhat inflexible, e.g. it is hard to modify color scales or plotting parameters. If you require more control over plotting, it is better to convert the object to a \code{data.frame} first and use the standard functions for plotting. } \section{Methods (by class)}{ \itemize{ \item \code{x = dimRedData,y = ANY}: Ploting of dimRedData objects \item \code{x = dimRedResult,y = ANY}: Ploting of dimRedResult objects. }} \examples{ scurve = loadDataSet("3D S Curve") plot(scurve, type = "pairs", main = "pairs plot of S curve") plot(scurve, type = "parpl") plot(scurve, type = "2vars", vars = c("y", "z")) plot(scurve, type = "3vars") } dimRed/man/reconstruction_rmse-dimRedResult-method.Rd0000644000176200001440000000227013753034327022516 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/quality.R \name{reconstruction_rmse,dimRedResult-method} \alias{reconstruction_rmse,dimRedResult-method} \alias{reconstruction_rmse} \title{Method reconstruction_rmse} \usage{ \S4method{reconstruction_rmse}{dimRedResult}(object) } \arguments{ \item{object}{of class dimRedResult} } \description{ Calculate the reconstruction root mean squared error a dimensionality reduction, the method must have an inverse mapping. } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{plot_R_NX}()}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/FruchtermanReingold-class.Rd0000644000176200001440000000452013753034327017575 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/graph_embed.R \docType{class} \name{FruchtermanReingold-class} \alias{FruchtermanReingold-class} \alias{FruchtermanReingold} \title{Fruchterman Reingold Graph Layout} \description{ An S4 Class implementing the Fruchterman Reingold Graph Layout algorithm. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ \describe{ \item{ndim}{The number of dimensions, defaults to 2. Can only be 2 or 3} \item{knn}{Reduce the graph to keep only the neares neighbors. Defaults to 100.} \item{d}{The distance function to determine the weights of the graph edges. Defaults to euclidean distances.} } } \section{Implementation}{ Wraps around \code{\link[igraph]{layout_with_fr}}, see there for details. The Fruchterman Reingold algorithm puts the data into a circle and puts connected points close to each other. } \examples{ dat <- loadDataSet("Swiss Roll", n = 100) emb <- embed(dat, "FruchtermanReingold") plot(emb, type = "2vars") } \references{ Fruchterman, T.M.J., Reingold, E.M., 1991. Graph drawing by force-directed placement. Softw: Pract. Exper. 21, 1129-1164. https://doi.org/10.1002/spe.4380211102 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FastICA-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/man/print.Rd0000644000176200001440000000047713065033470013665 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/misc.R \name{print} \alias{print} \title{Method print} \usage{ print(x, ...) } \arguments{ \item{x}{The object to be printed.} \item{...}{Other arguments for printing.} } \description{ Imports the print method into the package namespace. } dimRed/man/plot_R_NX.Rd0000644000176200001440000000425213753034327014376 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plot.R \name{plot_R_NX} \alias{plot_R_NX} \title{plot_R_NX} \usage{ plot_R_NX(x, ndim = NA, weight = "inv") } \arguments{ \item{x}{a list of \code{\link{dimRedResult}} objects. The names of the list will appear in the legend with the AUC_lnK value.} \item{ndim}{the number of dimensions, if \code{NA} the original number of embedding dimensions is used, can be a vector giving the embedding dimensionality for each single list element of \code{x}.} \item{weight}{the weight function used for K when calculating the AUC, one of \code{c("inv", "log", "log10")}} } \value{ A ggplot object, the design can be changed by appending \code{theme(...)} } \description{ Plot the R_NX curve for different embeddings. Takes a list of \code{\link{dimRedResult}} objects as input. Also the Area under the curve values are computed for a weighted K (see \link{AUC_lnK_R_NX} for details) and appear in the legend. } \examples{ ## define which methods to apply embed_methods <- c("Isomap", "PCA") ## load test data set data_set <- loadDataSet("3D S Curve", n = 200) ## apply dimensionality reduction data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) names(data_emb) <- embed_methods ## plot the R_NX curves: plot_R_NX(data_emb) + ggplot2::theme(legend.title = ggplot2::element_blank(), legend.position = c(0.5, 0.1), legend.justification = c(0.5, 0.1)) } \seealso{ Other Quality scores for dimensionality reduction: \code{\link{AUC_lnK_R_NX,dimRedResult-method}}, \code{\link{LCMC,dimRedResult-method}}, \code{\link{Q_NX,dimRedResult-method}}, \code{\link{Q_global,dimRedResult-method}}, \code{\link{Q_local,dimRedResult-method}}, \code{\link{R_NX,dimRedResult-method}}, \code{\link{cophenetic_correlation,dimRedResult-method}}, \code{\link{distance_correlation,dimRedResult-method}}, \code{\link{mean_R_NX,dimRedResult-method}}, \code{\link{quality,dimRedResult-method}}, \code{\link{reconstruction_error,dimRedResult-method}}, \code{\link{reconstruction_rmse,dimRedResult-method}}, \code{\link{total_correlation,dimRedResult-method}} } \concept{Quality scores for dimensionality reduction} dimRed/man/FastICA-class.Rd0000644000176200001440000000451413753034327015050 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/fastica.R \docType{class} \name{FastICA-class} \alias{FastICA-class} \alias{FastICA} \title{Independent Component Analysis} \description{ An S4 Class implementing the FastICA algorithm for Indepentend Component Analysis. } \details{ ICA is used for blind signal separation of different sources. It is a linear Projection. } \section{Slots}{ \describe{ \item{\code{fun}}{A function that does the embedding and returns a dimRedResult object.} \item{\code{stdpars}}{The standard parameters for the function.} }} \section{General usage}{ Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the \code{@fun()} slot, or the method name be passed to the embed function and parameters can be given to the \code{...}, in which case missing parameters will be replaced by the ones in the \code{@stdpars}. } \section{Parameters}{ FastICA can take the following parameters: \describe{ \item{ndim}{The number of output dimensions. Defaults to \code{2}} } } \section{Implementation}{ Wraps around \code{\link[fastICA]{fastICA}}. FastICA uses a very fast approximation for negentropy to estimate statistical independences between signals. Because it is a simple rotation/projection, forward and backward functions can be given. } \examples{ dat <- loadDataSet("3D S Curve") emb <- embed(dat, "FastICA", ndim = 2) plot(getData(getDimRedData(emb))) } \references{ Hyvarinen, A., 1999. Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10, 626-634. https://doi.org/10.1109/72.761722 } \seealso{ Other dimensionality reduction methods: \code{\link{AutoEncoder-class}}, \code{\link{DRR-class}}, \code{\link{DiffusionMaps-class}}, \code{\link{DrL-class}}, \code{\link{FruchtermanReingold-class}}, \code{\link{HLLE-class}}, \code{\link{Isomap-class}}, \code{\link{KamadaKawai-class}}, \code{\link{LLE-class}}, \code{\link{MDS-class}}, \code{\link{NNMF-class}}, \code{\link{PCA-class}}, \code{\link{PCA_L1-class}}, \code{\link{UMAP-class}}, \code{\link{dimRedMethod-class}}, \code{\link{dimRedMethodList}()}, \code{\link{kPCA-class}}, \code{\link{nMDS-class}}, \code{\link{tSNE-class}} } \concept{dimensionality reduction methods} dimRed/DESCRIPTION0000644000176200001440000000301014153365332013163 0ustar liggesusersPackage: dimRed Title: A Framework for Dimensionality Reduction Version: 0.2.4 Authors@R: c( person("Guido", "Kraemer", email = "guido.kraemer@uni-leipzig.de", role = c("aut", "cre")) ) Description: A collection of dimensionality reduction techniques from R packages and a common interface for calling the methods. Depends: R (>= 3.0.0), DRR Imports: magrittr, methods Suggests: NMF, MASS, Matrix, RANN, RSpectra, Rtsne, cccd, coRanking, diffusionMap, energy, fastICA, ggplot2, graphics, igraph, keras, kernlab, knitr, lle, loe, optimx, pcaL1, pcaPP, reticulate, rgl, scales, scatterplot3d, stats, tensorflow, testthat, tidyr, tinytex, umap, vegan VignetteBuilder: knitr License: GPL-3 | file LICENSE BugReports: https://github.com/gdkrmr/dimRed/issues URL: https://www.guido-kraemer.com/software/dimred/ Encoding: UTF-8 Collate: 'dimRedMethod-class.R' 'misc.R' 'dimRedData-class.R' 'dimRedResult-class.R' 'autoencoder.R' 'dataSets.R' 'diffmap.R' 'dimRed.R' 'drr.R' 'embed.R' 'fastica.R' 'get_info.R' 'graph_embed.R' 'hlle.R' 'isomap.R' 'kpca.R' 'l1pca.R' 'leim.R' 'lle.R' 'loe.R' 'mds.R' 'mixColorSpaces.R' 'nmds.R' 'nnmf.R' 'pca.R' 'plot.R' 'quality.R' 'rotate.R' 'soe.R' 'tsne.R' 'umap.R' RoxygenNote: 7.1.2 NeedsCompilation: yes Packaged: 2021-12-05 20:26:06 UTC; gkraemer Author: Guido Kraemer [aut, cre] Maintainer: Guido Kraemer Repository: CRAN Date/Publication: 2021-12-06 10:50:02 UTC dimRed/build/0000755000176200001440000000000014153220135012551 5ustar liggesusersdimRed/build/vignette.rds0000644000176200001440000000033314153220135015107 0ustar liggesusersb```b`adb`b2 1# 'IM+K,-JM)M.rJU%̂44R:^Xt%Z_g;<f&6̜TB2K7(1ݍ(\G^PT6@9XVr7) dimRed/tests/0000755000176200001440000000000014153220136012615 5ustar liggesusersdimRed/tests/testthat/0000755000176200001440000000000014153365332014465 5ustar liggesusersdimRed/tests/testthat/test_HLLE.R0000644000176200001440000000024713464507204016376 0ustar liggesuserscontext("HLLE") test_that("HLLE", { expect_error(embed(iris[1:4], "HLLE", ndim = 1, .mute = c("message", "output")), "ndim must be 2 or larger.") }) dimRed/tests/testthat/test_dimRedMethod-class.R0000644000176200001440000000071613464507204021323 0ustar liggesuserscontext("dimRedMethod-class") test_that("pars matching", { for (m in dimRedMethodList()) { mo <- getMethodObject(m) expect( all.equal( mo@stdpars, matchPars(mo, list()) ), paste("par matching for", m, "failed") ) } expect_warning( embed(iris[1:4], "PCA", asdf = 1234), "Parameter matching: asdf is not a standard parameter, ignoring." ) }) dimRed/tests/testthat/test_isomap.R0000644000176200001440000000210413371631672017140 0ustar liggesusers context("isomap") ## no isomap specific tests, because forward method is not really ## exact. test_that("check vs vegan isomap", { eps <- 1e-8 a <- loadDataSet("3D S Curve", n = 200) vegiso <- vegan::isomap(dist(getData(a)), k = 8, ndim = 2) vegy <- vegan::scores(vegiso) drdiso <- embed(a, "Isomap", knn = 8, ndim = 2) drdy <- drdiso@data@data ## Randomly fails: ## expect_equivalent(drdy, vegy) err1 <- max(abs(drdy - vegy)) drdy[, 2] <- -drdy[, 2] err2 <- max(abs(drdy - vegy)) drdy[, 1] <- -drdy[, 1] err3 <- max(abs(drdy - vegy)) drdy[, 2] <- -drdy[, 2] err4 <- max(abs(drdy - vegy)) err <- min(err1, err2, err3, err4) expect_true(err < eps, info = paste0("err = ", err, ", eps = ", eps, ", expected err < eps")) }) test_that("check other.data", { a <- loadDataSet("3D S Curve", n = 200) drdiso <- embed(a, "Isomap", knn = 8, ndim = 2, get_geod = TRUE) expect_true(inherits(getOtherData(drdiso)$geod, "dist")) }) dimRed/tests/testthat/test_diffmap.R0000644000176200001440000000053713464507204017262 0ustar liggesuserscontext("DiffusionMaps") test_that("DiffusionMaps", { expect_s4_class(embed(iris[1:4], "DiffusionMaps", ndim = 1, .mute = c("message", "output")), "dimRedResult") x <- embed(iris[1:4], "DiffusionMaps", ndim = 1, .mute = c("message", "output")) expect_equal(dim(x@data@data), c(150, 1)) }) dimRed/tests/testthat/test_umap.R0000644000176200001440000000376414153173664016630 0ustar liggesusers context("UMAP") skip_if_no_umap_learn <- function() { if (!reticulate::py_module_available("umap") && Sys.getenv("BNET_FORCE_UMAP_TESTS") != 1) skip("umap-learn not available, install with `pip install umap-learn==0.4`") } test_that("UMAP python", { skip_if_no_umap_learn() res1 <- embed(iris[1:4], "UMAP", .mute = c("message", "output")) res2 <- embed(iris[1:4], "UMAP", .mute = c("message", "output"), knn = 20) expect_s4_class(res1, "dimRedResult") expect_equal(res1@method, "UMAP") expect_equal(res1@pars$d, "euclidean") expect_equal(res1@pars$knn, 15) expect_equal(res1@pars$method, "umap-learn") expect_equal(res1@pars$ndim, 2) expect_s4_class(res2, "dimRedResult") expect_equal(res2@method, "UMAP") expect_equal(res2@pars$d, "euclidean") expect_equal(res2@pars$knn, 20) expect_equal(res2@pars$method, "umap-learn") expect_equal(res2@pars$ndim, 2) expect_true(any(res1@data@data != res2@data@data)) pred1 <- predict(res1, iris[1:4]) pred2 <- predict(res2, iris[1:4]) expect_equal(dim(pred1@data), dim(res1@data@data)) expect_equal(dim(pred2@data), dim(res2@data@data)) }) test_that("UMAP R", { res1 <- embed(iris[1:4], "UMAP", method = "naive", .mute = c("message", "output")) res2 <- embed(iris[1:4], "UMAP", method = "naive", .mute = c("message", "output"), knn = 20) expect_s4_class(res1, "dimRedResult") expect_equal(res1@method, "UMAP") expect_equal(res1@pars$d, "euclidean") expect_equal(res1@pars$knn, 15) expect_equal(res1@pars$method, "naive") expect_equal(res1@pars$ndim, 2) expect_s4_class(res2, "dimRedResult") expect_equal(res2@method, "UMAP") expect_equal(res2@pars$d, "euclidean") expect_equal(res2@pars$knn, 20) expect_equal(res2@pars$method, "naive") expect_equal(res2@pars$ndim, 2) expect_true(any(res1@data@data != res2@data@data)) pred1 <- predict(res1, iris[1:4]) pred2 <- predict(res2, iris[1:4]) expect_equal(dim(pred1@data), dim(res1@data@data)) expect_equal(dim(pred2@data), dim(res2@data@data)) }) dimRed/tests/testthat/test_kPCA.R0000644000176200001440000000545513371631672016442 0ustar liggesusers data(iris) context("kPCA") test_that("general data conversions", { irisData <- loadDataSet("Iris") expect_equal(class(irisData)[1], "dimRedData") irisPars <- list() irisPars[[length(irisPars) + 1]] <- list(kernel = "rbfdot", kpar = list(sigma = 0.1)) irisPars[[length(irisPars) + 1]] <- list(kernel = "rbfdot", kpar = list(sigma = 1)) irisPars[[length(irisPars) + 1]] <- list(kernel = "polydot", kpar = list(degree = 3)) irisPars[[length(irisPars) + 1]] <- list(kernel = "vanilladot", kpar = list()) irisPars[[length(irisPars) + 1]] <- list(kernel = "laplacedot", kpar = list(sigma = 1)) irisPars[[length(irisPars) + 1]] <- list(kernel = "laplacedot", kpar = list(sigma = 0.1)) irisPars[[length(irisPars) + 1]] <- list(kernel = "besseldot", kpar = list(sigma = 0.1, order = 1, degree = 1)) irisPars[[length(irisPars) + 1]] <- list(kernel = "besseldot", kpar = list(sigma = 1, order = 2, degree = 3)) irisPars[[length(irisPars) + 1]] <- list(kernel = "splinedot", kpar = list()) irisRes <- lapply(irisPars, function(x) do.call( function(...) tryCatch(embed(.data = irisData, .method = "kPCA", ...), error = function(e) as.character(e)), x ) ) for (i in 1:length(irisRes)) { if (inherits(irisRes[[i]], "character")){ expect(grepl("singular", irisRes[[i]]), "singular") } else { expect(inherits(irisRes[[i]], "dimRedResult"), 'should be of class "dimRedResult"') } } ## This test fails with multithreaded blas ## for (i in 1:length(irisRes)){ ## if (inherits(irisRes[[i]], "dimRedResult")){ ## expect_equal(irisRes[[i]]@apply(irisData)@data[, 1:2], ## irisRes[[i]]@data@data) ## expect_equal(2, getNDim(irisRes[[i]])) ## ## the reverse is an approximate: ## expect_less_than( ## max( ## irisRes[[i]]@inverse(irisRes[[i]]@data)@data - irisData@data ## ), 300, ## ## paste0("inverse of kpca is an approximate, ", ## ## "so this may fail due to numerical inaccuracy") ## ) ## } ## } ## This one cannot calculate an inverse: kpca.fit <- embed(loadDataSet("3D S", n = 200), "kPCA", kernel = "splinedot", kpar = list()) expect( is.na(kpca.fit@inverse(1)), "The inverse should return NA" ) }) dimRed/tests/testthat/test_dimRedData.R0000644000176200001440000000260113371631672017650 0ustar liggesusers context("the dimRedData class") test_that("constructor", { expect_equal(dimRedData(), new("dimRedData", data = matrix(numeric(0), nrow = 0, ncol = 0), meta = data.frame())) expect_error(dimRedData(iris)) expect_s4_class(dimRedData(iris[, 1:4], iris[, 5]), "dimRedData") expect_s4_class(dimRedData(iris[, 1:4]), "dimRedData") expect_error(dimRedData(iris)) }) test_that("conversion functions", { expect_equal(as(iris[, 1:4], "dimRedData"), dimRedData(iris[, 1:4])) expect_error(as(iris, "dimRedData")) expect_equal(as(loadDataSet("Iris"), "data.frame"), as.data.frame(loadDataSet("Iris"))) expect_equivalent(as.dimRedData( Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, iris), loadDataSet("Iris") ) }) test_that("misc functions", { Iris <- loadDataSet("Iris") expect_equal(getData(Iris), Iris@data) expect_equal(getMeta(Iris), Iris@meta) ## No idea why this one is broken with --run-donttest --run-dontrun --timings ## Also broken for devtools::test("dimRed") expect_equal(nrow(Iris), 150) expect_equal(Iris[1:4], Iris[1:4, ]) expect_equal(Iris[1:4], Iris[c(rep(TRUE, 4), rep(FALSE, 146))]) expect_equal(Iris[1:4], Iris[c(rep(TRUE, 4), rep(FALSE, 146)), ]) }) dimRed/tests/testthat/test_PCA_L1.R0000644000176200001440000000645013464507273016621 0ustar liggesusers context("PCA L1") test_that("general data conversions", { skip_if_not_installed("pcaL1") irisData <- as(iris[, 1:4], "dimRedData") expect_equal(class(irisData)[1], "dimRedData") irisParsCS <- list(center = TRUE, .mute = c("message", "output"), ndim = 4, scale. = TRUE, projections = "l1", fun = "l1pca") irisParsC <- list(center = TRUE, .mute = c("message", "output"), ndim = 4, scale. = FALSE, projections = "l1", fun = "l1pca") irisParsS <- list(center = TRUE, .mute = c("message", "output"), ndim = 4, scale. = TRUE, projections = "l1", fun = "l1pcahp") irisPars <- list(center = FALSE, .mute = c("message", "output"), ndim = 4, scale. = FALSE, projections = "l1", fun = "l1pcastar") irisResCS <- do.call(function(...) embed(irisData, "PCA_L1", ...), irisParsCS) irisResS <- do.call(function(...) embed(irisData, "PCA_L1", ...), irisParsS) irisResC <- do.call(function(...) embed(irisData, "PCA_L1", ...), irisParsC) irisRes <- do.call(function(...) embed(irisData, "PCA_L1", ...), irisPars) expect_equal(4, getNDim(irisResCS)) expect_equal(4, getNDim(irisResS)) expect_equal(4, getNDim(irisResC)) expect_equal(4, getNDim(irisRes)) expect_equal(class(irisResCS)[1], "dimRedResult") expect_equal(class(irisResS)[1], "dimRedResult") expect_equal(class(irisResC)[1], "dimRedResult") expect_equal(class(irisRes)[1], "dimRedResult") expect_equal(irisResCS@apply(irisData), irisResCS@data) expect_equal(irisResS@apply(irisData), irisResS@data) expect_equal(irisResC@apply(irisData), irisResC@data) expect_equal(irisRes@apply(irisData), irisRes@data) expect(sqrt(mean( (irisResCS@inverse(irisResCS@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect(sqrt(mean( (irisResS@inverse(irisResS@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect(sqrt(mean( (irisResC@inverse(irisResC@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect(sqrt(mean( (irisRes@inverse(irisRes@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) scale2 <- function(x, center, scale.) scale(x, center, scale.) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisResCS), irisParsCS[c("center", "scale.")]), getData( getDimRedData(irisResCS) ), tolerance = 1e-2 ) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisResS), irisParsS[c("center", "scale.")]), getData( getDimRedData(irisResS) ), tolerance = 1e-2 ) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisResC), irisParsC[c("center", "scale.")]), getData( getDimRedData(irisResC) ), tolerance = 1e-2 ) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisRes), irisPars[c("center", "scale.")]), getData( getDimRedData(irisRes) ), tolerance = 1e-2 ) expect_s4_class({ embed(iris[1:4], "PCA_L1", ndim = 1, .mute = c("message", "output")) }, "dimRedResult") }) dimRed/tests/testthat/test_misc.R0000644000176200001440000000176013371631672016612 0ustar liggesuserscontext("misc functions") a <- matrix(rnorm(25), 5, 5) b <- matrix(rnorm(25), 5, 5) test_that("squared euclidean distance", { expect_equivalent( t(as.matrix(dist(rbind(a, b)))[6:10, 1:5] ^ 2), pdist2(a, b) ) }) test_that("formula functions", { expect_equal(rhs(a + b ~ c + d), ~ c + d + 0) expect_equal(lhs(a + b ~ c + d), ~ a + b + 0) }) test_that("makeEpsGraph", { check_makeEpsGraph <- function(x, eps){ naive <- as.matrix(dist(x)) naive[naive >= eps] <- 0 epsSp <- as.matrix(makeEpsSparseMatrix(x, eps)) all(naive == epsSp) } expect_true(check_makeEpsGraph(iris[1:4], 1000)) expect_true(check_makeEpsGraph(iris[1:4], 1)) expect_true(check_makeEpsGraph(iris[1:4], 0.5)) }) test_that("getRotationMatrixFail", { irisData <- as(iris[, 1:4], "dimRedData") expect_equal(class(irisData)[1], "dimRedData") irisRes <- embed(irisData, "tSNE") expect_error(getRotationMatrix(irisRes), "Not implemented for") }) dimRed/tests/testthat/test_embed.R0000644000176200001440000000017213371631672016727 0ustar liggesusers context("embed") test_that("standard method is PCA", { res <- embed(iris[1:4]) expect_equal(res@method, "PCA") }) dimRed/tests/testthat/test_drr.R0000644000176200001440000000052313371631672016442 0ustar liggesusers context("DRR") test_that("drr forward and backward passes", { spiral <- loadDataSet("Helix", n = 200) drr_spiral <- embed(spiral, "DRR", ndim = 3, .mute = c("message", "output")) expect_equal(3, getNDim(drr_spiral)) dsa <- drr_spiral@apply(spiral) dsi <- drr_spiral@inverse(dsa) expect_equal(dsi, spiral) }) dimRed/tests/testthat/test_PCA.R0000644000176200001440000000504513142050030016235 0ustar liggesusers context("PCA") test_that("general data conversions", { irisData <- as(iris[, 1:4], "dimRedData") expect_equal(class(irisData)[1], "dimRedData") irisParsCS <- list(center = TRUE, scale. = TRUE) irisParsC <- list(center = TRUE, scale. = FALSE) irisParsS <- list(center = FALSE, scale. = TRUE) irisPars <- list(center = FALSE, scale. = FALSE) irisResCS <- do.call(function(...) embed(irisData, "PCA", ...), irisParsCS) irisResS <- do.call(function(...) embed(irisData, "PCA", ...), irisParsS) irisResC <- do.call(function(...) embed(irisData, "PCA", ...), irisParsC) irisRes <- do.call(function(...) embed(irisData, "PCA", ...), irisPars) expect_equal(2, getNDim(irisResCS)) expect_equal(2, getNDim(irisResS)) expect_equal(2, getNDim(irisResC)) expect_equal(2, getNDim(irisRes)) expect_equal(class(irisResCS)[1], "dimRedResult") expect_equal(class(irisResS)[1], "dimRedResult") expect_equal(class(irisResC)[1], "dimRedResult") expect_equal(class(irisRes)[1], "dimRedResult") expect_equal(irisResCS@apply(irisData), irisResCS@data) expect_equal(irisResS@apply(irisData), irisResS@data) expect_equal(irisResC@apply(irisData), irisResC@data) expect_equal(irisRes@apply(irisData), irisRes@data) expect(sqrt(mean( (irisResCS@inverse(irisResCS@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect(sqrt(mean( (irisResS@inverse(irisResS@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect(sqrt(mean( (irisResC@inverse(irisResC@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect(sqrt(mean( (irisRes@inverse(irisRes@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) scale2 <- function(x, center, scale.) scale(x, center, scale.) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisResCS), irisParsCS), getData( getDimRedData(irisResCS) ) ) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisResS), irisParsS), getData( getDimRedData(irisResS) ) ) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisResC), irisParsC), getData( getDimRedData(irisResC) ) ) expect_equal( do.call(function(...) scale2(iris[1:4], ...) %*% getRotationMatrix(irisRes), irisPars), getData( getDimRedData(irisRes) ) ) }) dimRed/tests/testthat/test_dimRedResult.R0000644000176200001440000000106613464507204020255 0ustar liggesusers context("dimRedResult-class") test_that("predict/inverse methods", { dat <- loadDataSet("Iris") emb <- embed(dat, "PCA", ndim = 4) pred <- predict(emb, dat) inv <- inverse(emb, pred) expect_equal(getDimRedData(emb), pred) expect_equal(dat, inv) emb2 <- embed(dat, "tSNE") expect_error(predict(emb2, dat)) expect_error(inverse(emb2, dat)) }) test_that("conversion", { iris_data_frame_as <- as(embed(loadDataSet("Iris"), "PCA"), "data.frame") expect_equal(colnames(iris_data_frame_as), c("meta.Species", "PC1", "PC2", colnames(iris)[-5])) }) dimRed/tests/testthat/test_NNMF.R0000644000176200001440000001255613464507273016424 0ustar liggesusersskip_if_no_NMF <- function() { if (!requireNamespace("NMF", quietly = TRUE) && Sys.getenv("BNET_FORCE_NNMF_TESTS") != "1") skip("NMF not available for testing") } context("NNMF") ## if we don't load the library explicitly, the predict function does not work ## (sometimes...). ## library(NMF) ints_trn <- matrix(seq(0, 98, by = 2), ncol = 5) input_trn <- dimRedData(as.data.frame(ints_trn)) input_tst <- dimRedData(ints_trn[1:3,] + 1) test_that("2D projection", { skip_if_no_NMF() dim_2_defaults <- embed(input_trn, "NNMF", seed = 13, nrun = 1) expect_equal(dim_2_defaults@method, "NNMF") ## Expected results from ## tmp <- NMF::nmf(t(ints_trn), rank = 2, nrun = 1, seed = 13) ## coefs <- basis(tmp) ## rownames(coefs) <- paste0("V", 1:5) ## colnames(coefs) <- paste0("NNMF", 1:2) ## coefs ## dput(coefs) dim_2_coef <- structure( c(18.807241710186, 30.2191667888959, 32.1069052462692, 9.53490906878683, 164.109205703974, 0.00064246562138093, 24.3924277525021, 56.4301459918642, 108.103923297376, 17.566220349863), .Dim = c(5L, 2L), .Dimnames = list(c("V1", "V2", "V3", "V4", "V5"), c("NNMF1", "NNMF2"))) expect_equivalent(dim_2_defaults@other.data$w, dim_2_coef) dim_2_apply <- dim_2_defaults@apply(input_tst)@data dim_2_pred <- predict(dim_2_defaults, input_tst)@data ## Expected results from ## t(solve(crossprod(basis(tmp)), t(input_tst@data %*% basis(tmp)))) ## preds <- getData(input_tst) %*% t(MASS::ginv(basis(tmp))) ## getData(getDimRedData(dim_2_defaults)) ## colnames(preds) <- paste0("NNMF", 1:2) ## dput(preds) dim_2_exp <- structure( c(0.427476458116875, 0.440237021147746, 0.452997584178617, 0.512256378881175, 0.5332094651398, 0.554162551398426), .Dim = c(3L, 2L), .Dimnames = list(NULL, c("NNMF1", "NNMF2")) ) expect_equivalent(dim_2_apply, dim_2_exp, tolerance = 0.01) expect_equivalent(dim_2_pred, dim_2_exp, tolerance = 0.01) }) test_that("other arguments", { skip_if_no_NMF() dim_3_args <- embed(input_trn, "NNMF", seed = 13, nrun = 10, ndim = 3, method = "KL", options = list(.pbackend = NULL)) ## Expected results from ## tmp <- NMF::nmf(t(ints_trn), rank = 3, nrun = 10, seed = 13, ## method = "KL", .pbackend = NULL) ## coefs <- t(NMF::coef(tmp)) ## colnames(coefs) <- paste0("NNMF", 1:ncol(coefs)) ## coefs ## dput(coefs) ## rot <- NMF::basis(tmp) ## rownames(rot) <- paste0("V", 1:nrow(rot)) ## dput(rot) dim_3_rot <- structure( c(11.624951277152, 31.2554213278975, 50.8858913786408, 70.5163614293837, 90.1468314801264, 2.22044604925031e-16, 36.4357899711133, 72.8715799422292, 109.307369913346, 145.743159884462, 22.4019808842378, 42.1081005773292, 61.8142202704197, 81.52033996351, 101.2264596566), .Dim = c(5L, 3L), .Dimnames = list(c("V1", "V2", "V3", "V4", "V5"), NULL) ) dim_3_pred <- structure( c(2.22044604925031e-16, 0.0731742704517501, 0.194863499580201, 0.50224638618713, 0.557517908619563, 0.197219538171418, 0.0860784848917408, 0.159094934700865, 0.10366866301249, 0.216483929440989, 0.54891083782883, 0.481738298195276, 0.40204352636632, 0.274419226004639, 0.211867578024856, 0.256578985276104, 0.236980211423017, 0.16984840699324, 0.135869049278152, 0.0584647425861749, 2.22044604925031e-16, 0.0513058500137363, 0.0774360678481537, 0.00720517673339281, 0.0678012129377125, 0.344046917890136, 0.49099862480747, 0.542386371921862, 0.660426277478513, 0.691161417731563), .Dim = c(10L, 3L), .Dimnames = list(NULL, c("NNMF1", "NNMF2", "NNMF3")) ) expect_equivalent(dim_3_args@other.data$w, dim_3_rot) expect_equivalent(getData(getDimRedData(dim_3_args)), dim_3_pred) dim_3_apply <- dim_3_args@apply(input_tst)@data dim_3_pred <- predict(dim_3_args, input_tst)@data ## Expected results from ## crossprod(basis(tmp)) does not have full rank!!! This needs to be considered ## w <- getOtherData(dim_3_args)$w ## preds <- t(solve(crossprod(w), t(input_trn@data %*% w))) ## preds <- t(qr.solve(crossprod(w), t(input_trn@data %*% w))) ## preds <- getData(input_tst) %*% t(MASS::ginv(w)) ## preds ## dput(preds) ## getData(getDimRedData(dim_3_args)) ## preds - getData(getDimRedData(dim_3_args)) ## input_trn@data ## input_tst@data %*% basis(tmp) ## colnames(preds) <- paste0("NNMF", 1:3) dim_3_exp <- structure( c(0.118730450278164, 0.144080695556738, 0.169430940835312, 0.494122495652466, 0.439293850852014, 0.384465206051563, -0.0169733070286198, 0.0591496323928872, 0.135272571814394), .Dim = c(3L, 3L) ) expect_equivalent(dim_3_apply, dim_3_exp, tolerance = 0.01) expect_equivalent(dim_3_pred, dim_3_exp, tolerance = 0.01) }) test_that("Bad args", { skip_if_no_NMF() expect_error(embed(iris, "NNMF")) expect_error(embed(iris[, 1], "NNMF"), "`ndim` should be less than the number of columns") expect_error(embed(iris[1:4], "NNMF", method = c("a", "b")), "only supply one `method`") expect_error(embed(scale(iris[1:4]), "NNMF"), "negative entries") }) test_that("Full_rank", { dim_2_full_rank_example <- embed(input_trn, "NNMF", ndim = ncol(input_trn@data)) dim_2_recon <- inverse(dim_2_full_rank_example, dim_2_full_rank_example@data@data) expect_equivalent(dim_2_recon, input_trn) }) dimRed/tests/testthat/test_ICA.R0000644000176200001440000000121113142050040016216 0ustar liggesusers context("FastICA") test_that("general data conversions", { irisData <- as(iris[, 1:4], "dimRedData") expect_equal(class(irisData)[1], "dimRedData") irisRes <- embed(irisData, "FastICA") expect_equal(class(irisRes)[1], "dimRedResult") expect_equal(2, getNDim(irisRes)) expect_equal(irisRes@apply(irisData), irisRes@data) expect(sqrt(mean( (irisRes@inverse(irisRes@data)@data - irisData@data) ^ 2 )) < 0.3, "error too large" ) expect_equal( scale(iris[1:4], TRUE, FALSE) %*% getRotationMatrix(irisRes), unname(as.matrix(getData( getDimRedData(irisRes) )) ) ) }) dimRed/tests/testthat/test_autoencoder.R0000644000176200001440000002234314153207515020161 0ustar liggesusers context("AutoEncoder") skip_if_no_tensorflow <- function() { if (!reticulate::py_module_available("tensorflow") && Sys.getenv("BNET_FORCE_AUTOENCODER_TESTS") != "1") skip("TensorFlow not available for testing") } skip_if_no_keras <- function() { if (!keras::is_keras_available() && Sys.getenv("BNET_FORCE_AUTOENCODER_TESTS") != "1") skip("Keras not available for testing") } test_that("Check if tensorflow is installed correctly.", { skip_if_no_tensorflow() library(tensorflow) tensorflow::tf$compat$v1$disable_v2_behavior() # I have not found a way to suppress the warning tf gives on first use. sess <- tf$compat$v1$Session() hello <- "Hello, TensorFlow!" tf_hello <- tf$compat$v1$constant(hello) tf_hello_res <- sess$run(tf_hello) # in python 3 this returns a `bytes` object $decode() transforms it into a # sting, in python 2 this is a simple string if(!is.character(tf_hello_res)) tf_hello_res <- tf_hello_res$decode() ## print("tf_hello_res:") ## print(str(tf_hello_res)) ## print(tf_hello_res) expect(tf_hello_res == hello, paste("tensorflow does not work:\n", "hello =", hello, "\n", "sess$run(tf_hello) =", tf_hello_res)) }) test_that("Check errors when building autoencoder.", { skip_if_no_tensorflow() iris_data <- as(iris[, 1:4], "dimRedData") expect_error(embed(iris_data, "AutoEncoder", activation = "sigmoid"), "declare an activation function for each layer") expect_error(embed(iris_data, "AutoEncoder", n_hidden = c(1, 2, 2, 1)), "the number of layers must be impair") expect_error(embed(iris_data, "AutoEncoder", weight_decay = -1), "weight decay must be > 0") expect_error(embed(iris_data, "AutoEncoder", learning_rate = -1), "learning rate must be > 0") expect_error(embed(iris_data, "AutoEncoder", n_steps = -1), "n_steps must be > 0") expect_error(embed(iris_data, "AutoEncoder", n_hidden = c(4, 2, 4), ndim = 3), "the middle of n_hidden must be equal to ndim") }) test_that("using autoencoder with parameters", { skip_if_no_tensorflow() iris_data <- as(iris[, 1:4], "dimRedData") expect_equal(class(iris_data)[1], "dimRedData") ae <- lapply(1:2, function(x) embed(iris_data, "AutoEncoder", n_hidden = c(10, x, 10), ndim = x, n_steps = 100)) aq <- lapply(ae, function(x) quality(x, "reconstruction_rmse")) lapply(ae, function(x) expect_s4_class(x, "dimRedResult")) ## expect(aq[[1]] > aq[[2]], "the error should decrease with more dimensions") ## expect(aq[[2]] > aq[[3]], "the error should decrease with more dimensions") ## expect(aq[[3]] > aq[[4]], "the error should decrease with more dimensions") lapply(1:length(ae), function(x) expect_equal(x, getNDim(ae[[x]]))) ae <- lapply(1:2, function(x) embed(iris_data, "AutoEncoder", n_hidden = c(10, x, 10), ndim = x, weight_decay = 0.1, n_steps = 100)) aq <- lapply(ae, function(x) quality(x, "reconstruction_rmse")) lapply(ae, function(x) expect_s4_class(x, "dimRedResult")) ## expect(aq[[1]] > aq[[2]], "the error should decrease with more dimensions") ## expect(aq[[2]] > aq[[3]], "the error should decrease with more dimensions") ## expect(aq[[3]] > aq[[4]], "the error should decrease with more dimensions") lapply(1:length(ae), function(x) expect_equal(x, getNDim(ae[[x]]))) ae <- lapply(1:2, function(x) embed(iris_data, "AutoEncoder", n_hidden = c(10, x, 10), ndim = x, learning_rate = 0.1, weight_decay = 0.1, n_steps = 100)) aq <- lapply(ae, function(x) quality(x, "reconstruction_rmse")) lapply(ae, function(x) expect_s4_class(x, "dimRedResult")) ## expect(aq[[1]] > aq[[2]], "the error should decrease with more dimensions") ## expect(aq[[2]] > aq[[3]], "the error should decrease with more dimensions") ## expect(aq[[3]] > aq[[4]], "the error should decrease with more dimensions") lapply(1:length(ae), function(x) expect_equal(x, getNDim(ae[[x]]))) ae <- lapply(1:2, function(x) embed(iris_data, "AutoEncoder", n_hidden = c(10, x, 10), activation = c("sigmoid", "sigmoid", "sigmoid"), ndim = x, learning_rate = 0.1, weight_decay = 0.1, n_steps = 100)) aq <- lapply(ae, function(x) quality(x, "reconstruction_rmse")) lapply(ae, function(x) expect_s4_class(x, "dimRedResult")) aa <- lapply(c("tanh", "sigmoid", "relu", "elu"), function(x) embed(iris_data, "AutoEncoder", n_hidden = c(10, 2, 10), activation = c("sigmoid", "sigmoid", "sigmoid"), ndim = 2, learning_rate = 0.1, weight_decay = 0.1, n_steps = 100)) aaq <- lapply(aa, function(x) quality(x, "reconstruction_rmse")) lapply(aa, function(x) expect_s4_class(x, "dimRedResult")) ## expect(aq[[1]] > aq[[2]], "the error should decrease with more dimensions") ## expect(aq[[2]] > aq[[3]], "the error should decrease with more dimensions") ## expect(aq[[3]] > aq[[4]], "the error should decrease with more dimensions") lapply(1:length(ae), function(x) expect_equal(x, getNDim(ae[[x]]))) }) test_that("using autoencoder with autoencoder results", { skip_if_no_tensorflow() tensorflow::tf$compat$v1$set_random_seed(2) iris_data <- as(iris[, 1:4], "dimRedData") expect_equal(class(iris_data)[1], "dimRedData") ae1 <- lapply(1:2, function(x) embed(iris_data, "AutoEncoder", n_hidden = c(10, x, 10), ndim = x, n_steps = 1)) aq1 <- lapply(ae1, function(x) quality(x, "reconstruction_rmse")) ae2 <- lapply(ae1, function(x) embed(iris_data, "AutoEncoder", autoencoder = x, n_steps = 1000)) aq2 <- lapply(ae2, function(x) quality(x, "reconstruction_rmse")) lapply(ae1, function(x) expect_s4_class(x, "dimRedResult")) lapply(ae2, function(x) expect_s4_class(x, "dimRedResult")) expect(aq1[[1]] > aq2[[1]], "the error should decrease with more steps") expect(aq1[[2]] > aq2[[2]], "the error should decrease with more steps") ## expect(aq1[[3]] > aq2[[3]], "the error should decrease with more steps") ## expect(aq1[[4]] > aq2[[4]], "the error should decrease with more steps") lapply(1:length(ae1), function(x) expect_equal(x, getNDim(ae1[[x]]))) lapply(1:length(ae2), function(x) expect_equal(x, getNDim(ae2[[x]]))) }) test_that("using autoencoder with keras", { skip_if_no_tensorflow() skip_if_no_keras() encoder <- function(i) list(keras::layer_dense(units = 10, activation = "tanh"), keras::layer_dense(units = i)) decoder <- function() list(keras::layer_dense(units = 10, activation = "tanh"), keras::layer_dense(units = 4)) iris_data <- as(iris[, 1:4], "dimRedData") ae1 <- lapply(1:2, function(x) embed(iris_data, "AutoEncoder", keras_graph = list(encoder = encoder(x), decoder = decoder()), n_steps = 2)) aq1 <- lapply(ae1, function(x) quality(x, "reconstruction_rmse")) ae2 <- lapply(ae1, function(x) embed(iris_data, "AutoEncoder", autoencoder = x)) aq2 <- lapply(ae2, function(x) quality(x, "reconstruction_rmse")) lapply(ae1, function(x) expect_s4_class(x, "dimRedResult")) lapply(ae2, function(x) expect_s4_class(x, "dimRedResult")) ## expect(aq1[[1]] > aq2[[1]], "the error should decrease with more steps") ## expect(aq1[[2]] > aq2[[2]], "the error should decrease with more steps") ## expect(aq1[[3]] > aq2[[3]], "the error should decrease with more steps") ## expect(aq1[[4]] > aq2[[4]], "the error should decrease with more steps") lapply(1:length(ae1), function(x) expect_equal(x, getNDim(ae1[[x]]))) lapply(1:length(ae2), function(x) expect_equal(x, getNDim(ae2[[x]]))) }) ## test_that("garbage collection", { ## skip_if_no_tensorflow() ## tmp <- tf$get_session_handle(environment(ae[[1]]@apply)$dec) ## tmp <- tf$get_default_session() ## tmp$close ## tmp ## tf$get_session_handle() ## tf$Session() ## }) dimRed/tests/testthat/test_all.R0000644000176200001440000000305313373523703016421 0ustar liggesuserscontext("high level functions") test_that("high level functions working?", { embed_methods <- dimRedMethodList() quality_methods <- dimRedQualityList() scurve <- loadDataSet("3D S Curve", n = 300) for(i in 1:ncol(scurve@data)){ scurve@data[, i] <- scurve@data[, i] - min(scurve@data[, i]) } quality_results <- matrix(NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods)) embedded_data <- list() for (e in embed_methods) { message("embedding: ", e) if ((e != "AutoEncoder" || reticulate::py_module_available("tensorflow")) && (e != "UMAP" || reticulate::py_module_available("umap-learn")) && (e != "PCA_L1" || ("pcaL1" %in% rownames(installed.packages()))) ) { suppressWarnings( embedded_data[[e]] <- embed( scurve, e, .mute = c("message", "output"))) for (q in quality_methods) { message(" quality: ", q) quality_results[e, q] <- tryCatch( suppressWarnings(quality(embedded_data[[e]], q, .mute = c("message", "output"))), error = function (e) NA ) } } } lapply(embedded_data, function(x) expect_equal(2, getNDim(x))) expect(inherits(quality_results, "matrix"), "should be matrix") expect(storage.mode(quality_results) == "double", 'storage should be "double"') }) dimRed/tests/testthat/test_quality.R0000644000176200001440000000474213475160740017350 0ustar liggesusers context("quality") test_that("quality", { irisData <- loadDataSet("Iris") parsPCA <- list(center = TRUE, scale. = TRUE) resPCA <- do.call(function(...) embed(irisData, "PCA", ...), parsPCA) suppressWarnings( resQual <- list( Q_local(resPCA), Q_global(resPCA), mean_R_NX(resPCA), total_correlation(resPCA), cophenetic_correlation(resPCA), distance_correlation(resPCA), reconstruction_rmse(resPCA) ) ) lapply(resQual, function(x) expect_true(is.numeric(x))) }) test_that("Q_local ndim", { irisData <- loadDataSet("Iris") irisData <- irisData[!duplicated(irisData@data)] parsPCA <- list(center = TRUE, scale. = TRUE, ndim = 4) resPCA <- do.call(function(...) embed(irisData, "PCA", ...), parsPCA) tmp <- sapply(1:4, function(x) quality(resPCA, "Q_local", ndim = x)) expect_equal(rank(tmp), 1:4) }) test_that("rmse_by_ndim", { set.seed(1) ir <- loadDataSet("Iris") ir.drr <- embed(ir, "DRR", .mute = c("message", "output"), ndim = ndims(ir)) ir.pca <- embed(ir, "PCA", ndim = ndims(ir)) rmse_res <- data.frame( drr = reconstruction_error(ir.drr), pca = reconstruction_error(ir.pca) ) for (i in 1:length(rmse_res$pca)) { expect_true(rmse_res$pca[i] - rmse_res$drr[i] + 1e-12 > 0, info = paste0( "ndim = ", i, ", rmse pca = ", rmse_res$pca[i], ", rmse drr = ", rmse_res$drr[i] )) } # expect_true(all((rmse_res$pca - rmse_res$drr) + 1e-12 > 0)) expect_error(reconstruction_error(ir.pca, 5)) expect_error(reconstruction_error(ir.pca, 0)) }) test_that("AUC_lnK_R_NX", { irisData <- loadDataSet("Iris") irisData <- irisData[!duplicated(irisData@data)] parsPCA <- list(center = TRUE, scale. = TRUE, ndim = 4) resPCA <- do.call(function(...) embed(irisData, "PCA", ...), parsPCA) expect_true(length(AUC_lnK_R_NX(resPCA, weight = "inv")) == 1) expect_true(length(AUC_lnK_R_NX(resPCA, weight = "log")) == 1) expect_true(length(AUC_lnK_R_NX(resPCA, weight = "ln")) == 1) expect_true(length(AUC_lnK_R_NX(resPCA, weight = "log10")) == 1) expect_true(AUC_lnK_R_NX(resPCA, weight = "log") == AUC_lnK_R_NX(resPCA, weight = "ln")) expect_error(AUC_lnK_R_NX(resPCA, weight = "asdf")) }) dimRed/tests/testthat/test_dataSets.R0000644000176200001440000000030413024272076017412 0ustar liggesuserscontext("dataSets") test_that("datasets load", { for (d in dataSetList()) { ds <- loadDataSet(d) expect(inherits(ds, "dimRedData"), "must be of class 'dimRedData'") } }) dimRed/tests/testthat.R0000644000176200001440000000012513464507273014614 0ustar liggesuserslibrary(testthat) library(dimRed) test_check("dimRed", reporter = LocationReporter) dimRed/vignettes/0000755000176200001440000000000014153220136013463 5ustar liggesusersdimRed/vignettes/classification_tree.tex0000644000176200001440000000722513371631672020241 0ustar liggesusers\newcommand{\imp}[1] {\textbf{#1}} % style for implemented methods \newcommand{\noimp}[1] {#1} % style for not implemented methods \tikz[ % tree layout, grow cyclic, % level 1/.style={level distance=1.2cm, sibling angle=180, text width=1.5cm, font={\small}}, % level 2/.style={level distance=1.9cm, sibling angle=40, font={\scriptsize}},%, text width=1.4cm}, level 3/.style={level distance=2.2cm, sibling angle=30}, level 4/.style={level distance=2.3cm}, % text width=1.2cm, font=\tiny, innernode/.style={align=flush center},%, text width=1.2}, leaf/.style={% % draw, very thin, % fill=red!30, rounded corners, align=flush left, text width=, inner sep=2pt, font={\hangindent=0.2cm\scriptsize\sffamily}}, ]{ \node[innernode, draw, align=flush center, rounded corners, font={\normalsize\bfseries}]{ Dimensionality \\ reduction} child[] { node[innernode] {Convex} % level 1 child[sibling angle=55]{ node[innernode] {Full spectral} % level 2 child { node[innernode] {Euclidean distances} child { node[leaf, text width=1.3cm]{ \imp{PCA} \\ \imp{Classical scaling} } } } child { node[innernode] {Geodesic distances} child { node[leaf]{ \imp{Isomap} } } } child { node[innernode] {Kernel-based} child { node[leaf]{ \imp{Kernel PCA} \\ \noimp{MVU} } } } child { node[innernode] {Diffusion distance} child { node[leaf]{ \imp{Diffusion maps} } } } } child[] { node[innernode] {Removal of shared information by regression} %level 2 child{ node[leaf]{ \imp{DRR} } } } child[sibling angle=55] { node[innernode] {Sparse spectral} % level 2 child[sibling angle=45] { node[innernode] {Reconstruction weights} child {node[leaf]{ \imp{Local Linear Embedding} } } } child[sibling angle=45] { node[innernode] {Neighborhood graph Laplacian} child { node[leaf]{ \imp{Laplacian Eigenmaps} } } } child[sibling angle=45] { node[innernode] {Local tangent space} child { node[leaf, text width=2cm]{ \imp{Hessian LLE} \\ \noimp{Local tangent space alignment} } } } } } child[level distance=1.8cm] { node[innernode] {Non-convex} %level 1 child { node[innernode] {Weighted Euclidean distances} % level 2 child { node[leaf, text width=2cm]{ \imp{Non-linear MDS} \\ \noimp{Sammon's mapping} \\ \noimp{Stochastic Proximity Embedding} } } } child { node[innernode] {Alignment of local linear models} % level 2 child { node[leaf]{ \noimp{LLC} \\ \noimp{Man.\ charting} } } } child { node[innernode] {Neural network} % level 2 child { node[leaf]{ Autoencoder } } } child { node[innernode] {Discrete mapping} % level 2 child { node[leaf,text width=2.5cm]{ \noimp{Self Organizing Maps} \\ \noimp{Generative Topographic Mapping} \\ \noimp{Elastic Net} } } } child { node[innernode] {Stochastic methods} % level 2 child { node[leaf]{ \noimp{SNE} \\ \imp{t-SNE} \\ \noimp{NeRV} \\ \noimp{JNE} } } } child { node[innernode] {Force directed} % level 2 child { node[leaf, text width=2cm]{ \imp{Kamada-Kawai} \\ \imp{Fruchtermann-Reingold} \\ \imp{DrL} } } } }; } %%% Local Variables: %%% mode: LaTeX %%% TeX-command-extra-options: "-shell-escape" %%% TeX-engine: default %%% TeX-master: "dimensionality-reduction" %%% End:dimRed/vignettes/bibliography.bib0000644000176200001440000006220013371631672016630 0ustar liggesusers @book{rojo-alvarez_digital_2017, edition = {1st}, title = {Digital {Signal} {Processing} with {Kernel} {Methods}}, isbn = {978-1-118-61179-1}, publisher = 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The resulting low-dimensional data embeddings are often difficult to compare with objective criteria. % Here, we introduce the \CRANpkg{dimRed} and \CRANpkg{coRanking} packages for the R language. % These open source software packages enable users to easily access multiple classical and advanced DR methods using a common interface. % The packages also provide quality indicators for the embeddings and easy visualization of high dimensional data. % The \pkg{coRanking} package provides the functionality for assessing DR methods in the co-ranking matrix framework. % In tandem, these packages allow for uncovering complex structures high dimensional data. % Currently 15 DR methods are available in the package, some of which were not previously available to R users. % Here, we outline the \pkg{dimRed} and \pkg{coRanking} packages and make the implemented methods understandable to the interested reader. % } \section{Introduction} \label{sec:intro} Dimensionality Reduction (DR) essentially aims to find low dimensional representations of data while preserving their key properties. % Many methods exist in literature, optimizing different criteria: % maximizing the variance or the statistical independence of the projected data, % minimizing the reconstruction error under different constraints, % or optimizing for different error metrics, % just to name a few. % Choosing an inadequate method may imply that much of the underlying structure remains undiscovered. % Often the structures of interest in a data set can be well represented by fewer dimensions than exist in the original data. % Data compression of this kind has the additional benefit of making the encoded information better conceivable to our brains for further analysis tasks like classification or regression problems. % For example, the morphology of a plant's leaves, stems, and seeds reflect the environmental conditions the species usually grow in (e.g.,\ plants with large soft leaves will never grow in a desert but might have an advantage in a humid and shadowy environment). % Because the morphology of the entire plant depends on the environment, many morphological combinations will never occur in nature and the morphological space of all plant species is tightly constrained. % \citet{diaz_global_2016} found that out of six observed morphological characteristics only two embedding dimensions were enough to represent three quarters of the totally observed variability. % DR is a widely used approach for the detection of structure in multivariate data, and has applications in a variety of fields. % In climatology, DR is used to find the modes of some phenomenon, e.g.,\ the first Empirical Orthogonal Function of monthly mean sea surface temperature of a given region over the Pacific is often linked to the El Ni\~no Southern Oscillation or ENSO \citep[e.g.,\ ][]{hsieh_nonlinear_2004}. % In ecology the comparison of sites with different species abundances is a classical multivariate problem: each observed species adds an extra dimension, and because species are often bound to certain habitats, there is a lot of redundant information. Using DR is a popular technique to represent the sites in few dimensions, e.g.,\ \citet{aart_distribution_1972} matches wolfspider communities to habitat and \citet{morrall_soil_1974} match soil fungi data to soil types. (In ecology the general name for DR is ordination or indirect gradient analysis.) % Today, hyperspectral satellite imagery collects so many bands that it is very difficult to analyze and interpret the data directly. % Resuming the data into a set of few, yet independent, components is one way to reduce complexity \citep[e.g.,\ see][]{laparra_dimensionality_2015}. % DR can also be used to visualize the interiors of deep neural networks \citep[e.g.,\ see ][]{han_deep_2016}, where the high dimensionality comes from the large number of weights used in a neural network and convergence can be visualized by means of DR\@. % We could find many more example applications here but this is not the main focus of this publication. % The difficulty in applying DR is that each DR method is designed to maintain certain aspects of the original data and therefore may be appropriate for one task and inappropriate for another. % Most methods also have parameters to tune and follow different assumptions. The quality of the outcome may strongly depend on their tuning, which adds additional complexity. % DR methods can be modeled after physical models with attracting and repelling forces (Force Directed Methods), projections onto low dimensional planes (PCA, ICA), divergence of statistical distributions (SNE family), or the reconstruction of local spaces or points by their neighbors (LLE). % As an example for how changing internal parameters of a method can have a great impact, the breakthrough for Stochastic Neighborhood Embedding (SNE) methods came when a Student's $t$-distribution was used instead of a normal distribution to model probabilities in low dimensional space to avoid the ``crowding problem'', that is,\ a sphere in high dimensional space has a much larger volume than in low dimensional space and may contain too many points to be represented accurately in few dimensions. % The $t$-distribution, allows medium distances to be accurately represented in few dimensions by larger distances due to its heavier tails. % The result is called in $t$-SNE and is especially good at preserving local structures in very few dimensions, this feature made $t$-SNE useful for a wide array of data visualization tasks and the method became much more popular than standard SNE (around six times more citations of \citet{van_der_maaten_visualizing_2008} compared to \citet{hinton_stochastic_2003} in Scopus \citep{noauthor_scopus_nodate}). % There are a number of software packages for other languages providing collections of methods: In Python there is scikit-learn \citep{scikit-learn}, which contains a module for DR. In Julia we currently find ManifoldLearning.jl for nonlinear and MultivariateStats.jl for linear DR methods. % There are several toolboxes for DR implemented in Matlab \citep{van_der_maaten_dimensionality_2009, arenas-garcia_kernel_2013}. The Shogun toolbox \citep{soeren_sonnenburg_2017_1067840} implements a variety of methods for dimensionality reduction in C++ and offers bindings for a many common high level languages (including R, but the installation is anything but simple, as there is no CRAN package). % However, there is no comprehensive package for R and none of the former mentioned software packages provides means to consistently compare the quality of different methods for DR. % For many applications it can be difficult to objectively find the right method or parameterization for the DR task. % This paper presents the \pkg{dimRed} and \pkg{coRanking} packages for the popular programming language R. Together, they provide a standardized interface to various dimensionality reduction methods and quality metrics for embeddings. They are implemented using the S4 class system of R, making the packages both easy to use and to extend. The design goal for these packages is to enable researchers, who may not necessarily be experts in DR, to apply the methods in their own work and to objectively identify the most suitable methods for their data. % This paper provides an overview of the methods collected in the packages and contains examples as to how to use the packages. % The notation in this paper will be as follows: $X = [x_i]_{1\leq i \leq n}^T \in \mathbb{R}^{n\times p}$, and the observations $x_i \in \mathbb{R}^p$. % These observations may be transformed prior to the dimensionality reduction step (e.g.,\ centering and/or standardization) resulting in $X' = [x'_i]_{1\leq i \leq n}^T \in \mathbb{R}^{n\times p}$. % A DR method then embeds each vector in $X'$ onto a vector in $Y = [y_i]_{1\leq i \leq n}^T \in \mathbb{R}^{n\times q}$ with $y_i \in \mathbb{R}^q$, ideally with $q \ll p$. % Some methods provide an explicit mapping $f(x'_i) = y_i$. Some even offer an inverse mapping $f^{-1}(y_{i}) = \hat x'_{i}$, such that one can reconstruct a (usually approximate) sample from the low-dimensional representation. % For some methods, pairwise distances between points are needed, we set $d_{ij} = d(x_{i}, x_{j})$ and $\hat{d}_{ij} = d(y_i, y_j)$, where $d$ is some appropriate distance function. When referring to \code{functions} in the \pkg{dimRed} package or base R simply the function name is mentioned, functions from other packages are referenced with their namespace, as with \code{package::function}. \begin{figure}[htbp] \centering \input{classification_tree.tex} \caption{% Classification of dimensionality reduction methods. Methods in bold face are implemented in \pkg{dimRed}. Modified from \citet{van_der_maaten_dimensionality_2009}. }\label{fig:classification} \end{figure} \section{Dimensionality Reduction Methods} \label{sec:dimredtec} In the following section we do not aim for an exhaustive explanation to every method in \pkg{dimRed} but rather to provide a general idea on how the methods work. % An overview and classification of the most commonly used DR methods can be found in Figure~\ref{fig:classification}. In all methods, parameters have to be optimized or decisions have to be made, even if it is just about the preprocessing steps of data. % The \pkg{dimRed} package tries to make the optimization process for parameters as easy as possible, but, if possible, the parameter space should be narrowed down using prior knowledge. % Often decisions can be made based on theoretical knowledge. For example,\ sometimes an analysis requires data to be kept in their original scales and sometimes this is exactly what has to be avoided as when comparing different physical units. % Sometimes decisions based on the experience of others can be made, e.g.,\ the Gaussian kernel is probably the most universal kernel and therefore should be tested first if there is a choice. % All methods presented here have the embedding dimensionality, $q$, as a parameter (or \code{ndim} as a parameter for \code{embed}). % For methods based on eigenvector decomposition, the result generally does not depend on the number of dimensions, i.e.,\ the first dimension will be the same, no matter if we decide to calculate only two dimensions or more. % If more dimensions are added, more information is maintained, the first dimension is the most important and higher dimensions are successively less important. % This means, that a method based on eigenvalue decomposition only has to be run once if one wishes to compare the embedding in different dimensions. % In optimization based methods this is generally not the case, the number of dimensions has to be chosen a priori, an embedding of 2 and 3 dimensions may vary significantly, and there is no ordered importance of dimensions. % This means that comparing dimensions of optimization-based methods is computationally much more expensive. % We try to give the computational complexity of the methods. Because of the actual implementation, computation times may differ largely. % R is an interpreted language, so all parts of an algorithm that are implemented in R often will tend to be slow compared to methods that call efficient implementations in a compiled language. % Methods where most of the computing time is spent for eigenvalue decomposition do have very efficient implementations as R uses optimized linear algebra libraries. Although, eigenvalue decomposition itself does not scale very well in naive implementations ($\mathcal{O}(n^3)$). \subsection{PCA} \label{sec:pca} Principal Component Analysis (PCA) is the most basic technique for reducing dimensions. It dates back to \citet{pearson_lines_1901}. PCA finds a linear projection ($U$) of the high dimensional space into a low dimensional space $Y = XU$, maintaining maximum variance of the data. It is based on solving the following eigenvalue problem: \begin{equation} (C_{XX}-\lambda_k I)u_k=0\label{eq:pca} \end{equation} where $C_{XX} = \frac 1 n X^TX$ is the covariance matrix, $\lambda_k$ and $u_k$ are the $k$-th eigenvalue and eigenvector, and $I$ is the identity matrix. % The equation has several solutions for different values of $\lambda_k$ (leaving aside the trivial solution $u_k = 0$). % PCA can be efficiently applied to large data sets, because it computationally scales as $\mathcal{O}(np^2 + p^3)$, that is, it scales linearly with the number of samples and R uses specialized linear algebra libraries for such kind of computations. PCA is a rotation around the origin and there exist a forward and inverse mapping. % PCA may suffer from a scale problem, i.e.,\ when one variable dominates the variance simply because it is in a higher scale, to remedy this, the data can be scaled to zero mean and unit variance, depending on the use case, if this is necessary or desired. % Base R implements PCA in the functions \code{prcomp} and \code{princomp}; but several other implementations exist i.e., \BIOpkg{pcaMethods} from Bioconductor which implements versions of PCA that can deal with missing data. % The \pkg{dimRed} package wraps \code{prcomp}. \subsection{kPCA} \label{sec:kpca} Kernel Principal Component Analysis (kPCA) extends PCA to deal with nonlinear dependencies among variables. % The idea behind kPCA is to map the data into a high dimensional space using a possibly non-linear function $\phi$ and then to perform a PCA in this high dimensional space. % Some mathematical tricks are used for efficient computation. % If the columns of X are centered around $0$, then the principal components can also be computed from the inner product matrix $K = X^TX$. % Due to this way of calculating a PCA, we do not need to explicitly map all points into the high dimensional space and do the calculations there, it is enough to obtain the inner product matrix or kernel matrix $K \in \mathbb{R}^{n\times n}$ of the mapped points \citep{scholkopf_nonlinear_1998}. % Here is an example calculating the kernel matrix using a Gaussian kernel: \begin{equation}\label{eq:gauss} K = \phi(x_i)^T \phi(x_j) = \kappa(x_i, x_j) = \exp\left( -\frac{\| x_i- x_j\|^2}{2 \sigma^2} \right), \end{equation} where $\sigma$ is a length scale parameter accounting for the width of the kernel. % The other trick used is known as the ``representers theorem.'' The interested reader is referred to \citet{scholkopf_generalized_2001}. The kPCA method is very flexible and there exist many kernels for special purposes. The most common kernel function is the Gaussian kernel (Equation\ \ref{eq:gauss}). % The flexibility comes at the price that the method has to be finely tuned for the data set because some parameter combinations are simply unsuitable for certain data. % The method is not suitable for very large data sets, because memory scales with $\mathcal{O}(n^2)$ and computation time with $\mathcal{O}(n^3)$. % Diffusion Maps, Isomap, Locally Linear Embedding, and some other techniques can be seen as special cases of kPCA. In which case, an out-of-sample extension using the Nyström formula can be applied \citep{bengio_learning_2004}. % This can also yield applications for bigger data, where an embedding is trained with a sub-sample of all data and then the data is embedded using the Nyström formula. Kernel PCA in R is implemented in the \CRANpkg{kernlab} package using the function \code{kernlab::kpca}, and supports a number of kernels and user defined functions. For details see the help page for \code{kernlab::kpca}. The \pkg{dimRed} package wraps \code{kernlab::kpca} but additionally provides forward and inverse methods \citep{bakir_learning_2004} which can be used to fit out-of-sample data or to visualize the transformation of the data space. % \subsection{Classical Scaling} \label{sec:classscale} What today is called Classical Scaling was first introduced by \citet{torgerson_multidimensional_1952}. It uses an eigenvalue decomposition of a transformed distance matrix to find an embedding that maintains the distances of the distance matrix. % The method works because of the same reason that kPCA works, i.e.,\ classical scaling can be seen as a kPCA with kernel $x^Ty$. % A matrix of Euclidean distances can be transformed into an inner product matrix by some simple transformations and therefore yields the same result as a PCA\@. % Classical scaling is conceptually more general than PCA in that arbitrary distance matrices can be used, i.e.,\ the method does not even need the original coordinates, just a distance matrix $D$. % Then it tries to find an embedding $Y$ so that $\hat d_{ij}$ is as similar to $d_{ij}$ as possible. The disadvantage is that it is computationally much more demanding, i.e.,\ an eigenvalue decomposition of an $n\times n$ matrix has to be computed. This step requires $\mathcal{O}(n^2)$ memory and $\mathcal{O}(n^3)$ computation time, while PCA requires only the eigenvalue decomposition of a $d\times d$ matrix and usually $n \gg d$. % R implements classical scaling in the \code{cmdscale} function. % The \pkg{dimRed} package wraps \code{cmdscale} and allows the specification of arbitrary distance functions for calculating the distance matrix. Additionally a forward method is implemented. \subsection{Isomap} \label{sec:isomap} As Classical Scaling can deal with arbitrarily defined distances, \citet{tenenbaum_global_2000} suggested to approximate the structure of the manifold by using geodesic distances. % In practice, a graph is created by either keeping only the connections between every point and its $k$ nearest neighbors to produce a $k$-nearest neighbor graph ($k$-NNG), or simply by keeping all distances smaller than a value $\varepsilon$ producing an $\varepsilon$-neighborhood graph ($\varepsilon$-NNG). % Geodesic distances are obtained by recording the distance on the graph and classical scaling is used to find an embedding in fewer dimensions. This leads to an ``unfolding'' of possibly convoluted structures (see Figure~\ref{fig:knn}). Isomap's computational cost is dominated by the eigenvalue decomposition and therefore scales with $\mathcal{O}(n^3)$. % Other related techniques can use more efficient algorithms because the distance matrix becomes sparse due to a different preprocessing. In R, Isomap is implemented in the \CRANpkg{vegan} package. The \code{vegan::isomap} calculates an Isomap embedding and \code{vegan::isomapdist} calculates a geodesic distance matrix. % The \pkg{dimRed} package uses its own implementation. This implementation is faster mainly due to using a KD-tree for the nearest neighbor search (from the \CRANpkg{RANN} package) and to a faster implementation for the shortest path search in the $k$-NNG (from the \CRANpkg{igraph} package). % The implementation in \pkg{dimRed} also includes a forward method that can be used to train the embedding on a subset of data points and then use these points to approximate an embedding for the remaining points. This technique is generally referred to as landmark Isomap \citep{de_silva_sparse_2004}. % \subsection{Locally Linear Embedding} \label{sec:lle} Points that lie on a manifold in a high dimensional space can be reconstructed through linear combinations of their neighborhoods if the manifold is well sampled and the neighbohoods lie on a locally linear patch. % These reconstruction weights, $W$, are the same in the high dimensional space as the internal coordinates of the manifold. % Locally Linear Embedding \citep[LLE; ][]{roweis_nonlinear_2000} is a technique that constructs a weight matrix $W \in \mathbb{R}^{n\times n}$ with elements $w_{ij}$ so that \begin{equation} \sum_{i=1}^n \bigg\| x_i- \sum_{j=1}^{n} w_{ij}x_j \bigg\|^2\label{eq:lle} \end{equation} is minimized under the constraint that $w_{ij} = 0 $ if $x_j$ does not belong to the neighborhood and the constraint that $\sum_{j=1}^n w_{ij} = 1$. % Finally the embedding is made in such a way that the following cost function is minimized for $Y$, \begin{equation} \sum_{i=1}^n\bigg\| y_i - \sum_{j=1}^n w_{ij}y_j \bigg\|^2.\label{eq:lle2} \end{equation} This can be solved using an eigenvalue decomposition. Conceptually the method is similar to Isomap but it is computationally much nicer because the weight matrix is sparse and there exist efficient solvers. % In R, LLE is implemented by the package \CRANpkg{lle}, the embedding can be calculated with \code{lle::lle}. Unfortunately the implementation does not make use of the sparsity of the weight matrix $W$. % The manifold must be well sampled and the neighborhood size must be chosen appropriately for LLE to give good results. % \subsection{Laplacian Eigenmaps} \label{sec:laplaceigenmaps} Laplacian Eigenmaps were originally developed under the name spectral clustering to separate non-convex clusters. % Later it was also used for graph embedding and DR \citep{belkin_laplacian_2003}. % A number of variants have been proposed. % First, a graph is constructed, usually from a distance matrix, the graph can be made sparse by keeping only the $k$ nearest neighbors, or by specifying an $\varepsilon$ neighborhood. % Then, a similarity matrix $W$ is calculated by using a Gaussian kernel (see Equation \ref{eq:gauss}), if $c = 2 \sigma^2 = \infty$, then all distances are treated equally, the smaller $c$ the more emphasis is given to differences in distance. % The degree of vertex $i$ is $d_i = \sum_{j=1}^n w_{ij}$ and the degree matrix, $D$, is the diagonal matrix with entries $d_i$. % Then we can form the graph Laplacian $L = D - W$ and, then, there are several ways how to proceed, an overview can be found in \citet{luxburg_tutorial_2007}. % The \pkg{dimRed} package implements the algorithm from \citet{belkin_laplacian_2003}. Analogously to LLE, Laplacian eigenmaps avoid computational complexity by creating a sparse matrix and not having to estimate the distances between all pairs of points. % Then the eigenvectors corresponding to the lowest eigenvalues larger than $0$ of either the matrix $L$ or the normalized Laplacian $D^{-1/2}LD^{-1/2}$ are computed and form the embedding. \subsection{Diffusion Maps} \label{sec:isodiffmaplle} Diffusion Maps \citep{coifman_diffusion_2006} take a distance matrix as input and calculates the transition probability matrix $P$ of a diffusion process between the points to approximate the manifold. % Then the embedding is done by an eigenvalue decompositon of $P$ to calculate the coordinates of the embedding. % The algorithm for calculating Diffusion Maps shares some elements with the way Laplacian Eigenmaps are calculated. % Both algorithms depart from the same weight matrix, Diffusion Maps calculate the transition probability on the graph after $t$ time steps and do the embedding on this probability matrix. The idea is to simulate a diffusion process between the nodes of the graph, which is more robust to short-circuiting than the $k$-NNG from Isomap (see bottom right Figure \ref{fig:knn}). % Diffusion maps in R are accessible via the \code{diffusionMap::diffuse()} function, which is available in the \CRANpkg{diffusionMap} package. % Additional points can be approximated into an existing embedding using the Nyström formula \citep{bengio_learning_2004}. % The implementation in \pkg{dimRed} is based on the \code{diffusionMap::diffuse} function. % , which does not contain an % approximation for unequally sampled manifolds % \citep{coifman_geometric_2005}. % \subsection{non-Metric Dimensional Scaling} \label{sec:nmds} While Classical Scaling and derived methods (see section \nameref{sec:classscale}) use eigenvector decomposition to embed the data in such a way that the given distances are maintained, non-Metric Dimensional Scaling \citep[nMDS, ][]{kruskal_multidimensional_1964,kruskal_nonmetric_1964} uses optimization methods to reach the same goal. % Therefore a stress function, \begin{equation} \label{eq:stress} S = \sqrt{\frac{\sum_{i>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { library(dimRed); library(ggplot2); #library(dplyr); library(tidyr) ## define which methods to apply embed_methods <- c("Isomap", "PCA") ## load test data set data_set <- loadDataSet("3D S Curve", n = 1000) ## apply dimensionality reduction data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) names(data_emb) <- embed_methods ## plot data set, embeddings, and quality analysis ## plot(data_set, type = "3vars") ## lapply(data_emb, plot, type = "2vars") ## plot_R_NX(data_emb) add_label <- function(label) grid::grid.text(label, 0.2, 1, hjust = 0, vjust = 1, gp = grid::gpar(fontface = "bold", cex = 1.5)) ## pdf('~/phd/text/dimRedPackage/plots/plot_example.pdf', width = 4, height = 4) ## plot the results plot(data_set, type = "3vars", angle = 15, mar = c(3, 3, 0, 0), box = FALSE, grid = FALSE, pch = 16) add_label("a") par(mar = c(4, 4, 0, 0) + 0.1, bty = "n", las = 1) plot(data_emb$Isomap, type = "2vars", pch = 16) add_label("b") plot(data_emb$PCA, type = "2vars", pch = 16) add_label("d") ## calculate quality scores print( plot_R_NX(data_emb) + theme(legend.title = element_blank(), legend.position = c(0.5, 0.1), legend.justification = c(0.5, 0.1)) ) add_label("c") } else { # These cannot all be plot(1:10)!!! It's a mistery to me. plot(1:10) barplot(1:10) hist(1:10) plot(1:10) } @ \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-1.pdf} \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-2.pdf} \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-3.pdf} \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-4.pdf} \caption[dimRed example]{% Comparing PCA and Isomap: % (a) An S-shaped manifold, colors represent the internal coordinates of the manifold. % (b) Isomap embedding, the S-shaped manifold is unfolded. % (c) $R_{NX}$ plotted agains neighborhood sizes, Isomap is much better at preserving local distances and PCA is better at preserving global Euclidean distances. % The numbers on the legend are the $\text{AUC}_{1 / K}$. (d) PCA projection of the data, the directions of maximum variance are preserved. % }\label{fig:plotexample} \end{figure} <>= ## define which methods to apply embed_methods <- c("Isomap", "PCA") ## load test data set data_set <- loadDataSet("3D S Curve", n = 1000) ## apply dimensionality reduction data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) names(data_emb) <- embed_methods ## figure \ref{fig:plotexample}a, the data set plot(data_set, type = "3vars") ## figures \ref{fig:plotexample}b (Isomap) and \ref{fig:plotexample}d (PCA) lapply(data_emb, plot, type = "2vars") ## figure \ref{fig:plotexample}c, quality analysis plot_R_NX(data_emb) @ The function \code{plot\_R\_NX} produces a figure that plots the neighborhood size ($k$ at a log-scale) against the quality measure $\text{R}_{NX}(k)$ (see Equation \ref{eq:rnx}). % This gives an overview of the general behavior of methods: if $\text{R}_{NX}$ is high for low values of $K$, then local neighborhoods are maintained well; if $\text{R}_{NX}$ is high for large values of $K$, then global gradients are maintained well. % It also provides a way to directly compare methods by plotting more than one $\text{R}_{NX}$ curve and an overall quality of the embedding by taking the area under the curve as an indicator for the overall quality of the embedding (see fig~\ref{eq:auclnk}) which is shown as a number in the legend. Therefore we can see from Figure~\ref{fig:plotexample}c that $t$-SNE is very good a maintaining close and medium distances for the given data set, whereas PCA is only better at maintaining the very large distances. % The large distances are dominated by the overall bent shape of the S in 3D space, while the close distances are not affected by this bending. % This is reflected in the properties recovered by the different methods, the PCA embedding recovers the S-shape, while $t$-SNE ignores the S-shape and recovers the inner structure of the manifold. % Example 2: Often the quality of an embedding strongly depends on the choice of parameters, the interface of \pkg{dimRed} can be used to facilitate searching the parameter space. Isomap has one parameter $k$ which determines the number of neighbors used to construct the $k$-NNG\@. % If this number is too large, then Isomap will resemble an MDS (Figure~\ref{fig:knn} e), if the number is too small, the resulting embedding contains holes (Figure~\ref{fig:knn} c). % The following code finds the optimal value, $k_{\text{max}}$, for $k$ using the $Q_{\text{local}}$ criterion, the results are visualized in Figure~\ref{fig:knn} a: \begin{figure}[htp] \centering <>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { library(dimRed) library(cccd) ## Load data ss <- loadDataSet("3D S Curve", n = 500) ## Parameter space kk <- floor(seq(5, 100, length.out = 40)) ## Embedding over parameter space emb <- lapply(kk, function(x) embed(ss, "Isomap", knn = x)) ## Quality over embeddings qual <- sapply(emb, function(x) quality(x, "Q_local")) ## Find best value for K ind_max <- which.max(qual) k_max <- kk[ind_max] add_label <- function(label){ par(xpd = TRUE) b = par("usr") text(b[1], b[4], label, adj = c(0, 1), cex = 1.5, font = 2) par(xpd = FALSE) } names(qual) <- kk } @ <<"select_k",include=FALSE,fig.width=11,fig.height=5>>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { par(mfrow = c(1, 2), mar = c(5, 4, 0, 0) + 0.1, oma = c(0, 0, 0, 0)) plot(kk, qual, type = "l", xlab = "k", ylab = expression(Q[local]), bty = "n") abline(v = k_max, col = "red") add_label("a") plot(ss, type = "3vars", angle = 15, mar = c(3, 3, 0, 0), box = FALSE, grid = FALSE, pch = 16) add_label("b") } else { plot(1:10) plot(1:10) } @ <<"knngraphs",include=FALSE,fig.width=8,fig.height=3>>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { par(mfrow = c(1, 3), mar = c(5, 4, 0, 0) + 0.1, oma = c(0, 0, 0, 0)) add_knn_graph <- function(ind) { nn1 <- nng(ss@data, k = kk[ind]) el <- get.edgelist(nn1) segments(x0 = emb[[ind]]@data@data[el[, 1], 1], y0 = emb[[ind]]@data@data[el[, 1], 2], x1 = emb[[ind]]@data@data[el[, 2], 1], y1 = emb[[ind]]@data@data[el[, 2], 2], col = "#00000010") } plot(emb[[2]]@data@data, type = "n", bty = "n") add_knn_graph(2) points(emb[[2]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("c") plot(emb[[ind_max]]@data@data, type = "n", bty = "n") add_knn_graph(ind_max) points(emb[[ind_max]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("d") plot(emb[[length(emb)]]@data@data, type = "n", bty = "n") add_knn_graph(length(emb)) points(emb[[length(emb)]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("e") } else { plot(1:10) plot(1:10) plot(1:10) } @ \includegraphics[width=.95\textwidth]{figure/select_k-1.pdf} \includegraphics[width=.95\textwidth]{figure/knngraphs-1.pdf} \caption[estimating $k$ using @Q_\text{local}]{% Using \pkg{dimRed} and the $Q_\text{local}$ indicator to estimate a good value for the parameter $k$ in Isomap. % (a) $Q_\text{local}$ for different values of $k$, the vertical red line indicates the maximum $k_{\text{max}}$. % (b) The original data set, a 2 dimensional manifold bent in an S-shape in 3 dimensional space. % Bottom row: Embeddings and $k$-NNG for different values of $k$. % (c) When $k = 5$, the value for $k$ is too small resulting in holes in the embedding, the manifold itself is still unfolded correctly. % (d) Choose $k = k_\text{max}$, the best representation of the original manifold in two dimensions achievable with Isomap. % (e) $k = 100$, too large, the $k$-NNG does not approximate the manifold any more. % }\label{fig:knn} \end{figure} <>= ## Load data ss <- loadDataSet("3D S Curve", n = 500) ## Parameter space kk <- floor(seq(5, 100, length.out = 40)) ## Embedding over parameter space emb <- lapply(kk, function(x) embed(ss, "Isomap", knn = x)) ## Quality over embeddings qual <- sapply(emb, function(x) quality(x, "Q_local")) ## Find best value for K ind_max <- which.max(qual) k_max <- kk[ind_max] @ Figure~\ref{fig:knn}a shows how the $Q_{\text{local}}$ criterion changes when varying the neighborhood size $k$ for Isomap, the gray lines in Figure~\ref{fig:knn} represent the edges of the $k$-NN Graph. % If the value for $k$ is too low, the inner structure of the manifold will still be recovered, but it will be imperfect (Figure~\ref{fig:knn}c, note that the holes appear in places that are not covered by the edges of the $k$-NN Graph), therefore the $Q_{\text{local}}$ score is lower than optimal. % If $k$ is too large, the error of the embedding is much larger due to short circuiting and we observe a very steep drop in the $Q_{\text{local}}$ score. % The short circuiting can be observed in Figure~\ref{fig:knn}e with the edges that cross the gap between the tips and the center of the S-shape. % % Example 3: It is also very easy to compare across methods and quality scores. % The following code produces a matrix of quality scores and methods, where \code{dimRedMethodList} returns a character vector with all methods. A visualization of the matrix can be found in Figure~\ref{fig:qualityexample}. % \begin{figure}[htp] \centering <<"plot_quality",include=FALSE>>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { embed_methods <- dimRedMethodList() quality_methods <- c("Q_local", "Q_global", "AUC_lnK_R_NX", "cophenetic_correlation") iris_data <- loadDataSet("Iris") quality_results <- matrix( NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods) ) embedded_data <- list() for (e in embed_methods) { try(embedded_data[[e]] <- embed(iris_data, e)) for (q in quality_methods) try(quality_results[e,q] <- quality(embedded_data[[e]], q)) } quality_results <- quality_results[order(rowMeans(quality_results)), ] palette(c("#1b9e77", "#d95f02", "#7570b3", "#e7298a", "#66a61e")) col_hsv <- rgb2hsv(col2rgb(palette())) ## col_hsv["v", ] <- col_hsv["v", ] * 3 / 1 palette(hsv(col_hsv["h",], col_hsv["s",], col_hsv["v",])) par(mar = c(2, 8, 0, 0) + 0.1) barplot(t(quality_results), beside = TRUE, col = 1:4, legend.text = quality_methods, horiz = TRUE, las = 1, cex.names = 0.85, args.legend = list(x = "topleft", bg = "white", cex = 0.8)) } else { plot(1:10) } @ \includegraphics[width=.5\textwidth]{figure/plot_quality-1.pdf} \caption[Quality comparision]{% A visualization of the \code{quality\_results} matrix. % The methods are ordered by mean quality score. % The reconstruction error was omitted, because a higher value means a worse embedding, while in the present methods a higher score means a better embedding. % Parameters were not tuned for the example, therefore it should not be seen as a general quality assessment of the methods. % }\label{fig:qualityexample} \end{figure} <>= embed_methods <- dimRedMethodList() quality_methods <- c("Q_local", "Q_global", "AUC_lnK_R_NX", "cophenetic_correlation") scurve <- loadDataSet("3D S Curve", n = 2000) quality_results <- matrix( NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods) ) embedded_data <- list() for (e in embed_methods) { embedded_data[[e]] <- embed(scurve, e) for (q in quality_methods) try(quality_results[e, q] <- quality(embedded_data[[e]], q)) } @ This example showcases the simplicity with which different methods and quality criteria can be combined. % Because of the strong dependencies on parameters it is not advised to apply this kind of analysis without tuning the parameters for each method separately. % There is no automatized way to tune parameters in \pkg{dimRed}. % \section{Conclusion} \label{sec:conc} This paper presents the \pkg{dimRed} and \pkg{coRanking} packages and it provides a brief overview of the methods implemented therein. % The \pkg{dimRed} package is written in the R language, one of the most popular languages for data analysis. The package is freely available from CRAN. % The package is object oriented and completely open source and therefore easily available and extensible. % Although most of the DR methods already had implementations in R, \pkg{dimRed} adds some new methods for dimensionality reduction, and \pkg{coRanking} adds methods for an independent quality control of DR methods to the R ecosystem. % DR is a widely used technique. However, due to the lack of easily usable tools, choosing the right method for DR is complex and depends upon a variety of factors. % The \pkg{dimRed} package aims to facilitate experimentation with different techniques, parameters, and quality measures so that choosing the right method becomes easier. % The \pkg{dimRed} package wants to enable the user to objectively compare methods that rely on very different algorithmic approaches. % It makes the life of the programmer easier, because all methods are aggregated in one place and there is a single interface and standardized classes to access the functionality. % \section{Acknowledgments} \label{sec:ack} We thank Dr.\ G.\ Camps-Valls and an anonymous reviewer for many useful comments. % This study was supported by the European Space Agency (ESA) via the Earth System Data Lab project (\url{http://earthsystemdatacube.org}) and the EU via the H2020 project BACI, grant agreement No 640176. % \bibliographystyle{abbrvnat} \bibliography{bibliography} \end{document} dimRed/vignettes/Makefile0000644000176200001440000000043414153220136015124 0ustar liggesusersall: echo "BNET_BUILD_VIGNETTE: $(BNET_BUILD_VIGNETTE)" $(R_HOME)/bin/Rscript -e "knitr::knit2pdf('dimensionality-reduction.Rnw')" $(R_HOME)/bin/Rscript -e "tools::compactPDF('dimensionality-reduction.pdf', gs_quality = 'ebook')" rm -rf dimensionality-reduction.tex figure/ auto/ dimRed/R/0000755000176200001440000000000014153220136011654 5ustar liggesusersdimRed/R/diffmap.R0000644000176200001440000001067013562225201013412 0ustar liggesusers#' Diffusion Maps #' #' An S4 Class implementing Diffusion Maps #' #' Diffusion Maps uses a diffusion probability matrix to robustly #' approximate a manifold. #' #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' Diffusion Maps can take the following parameters: #' \describe{ #' \item{d}{a function transforming a matrix row wise into a #' distance matrix or \code{dist} object, #' e.g. \code{\link[stats]{dist}}.} #' \item{ndim}{The number of dimensions} #' \item{eps}{The epsilon parameter that determines the #' diffusion weight matrix from a distance matrix \code{d}, #' \eqn{exp(-d^2/eps)}, if set to \code{"auto"} it will #' be set to the median distance to the 0.01*n nearest #' neighbor.} #' \item{t}{Time-scale parameter. The recommended value, 0, #' uses multiscale geometry.} #' \item{delta}{Sparsity cut-off for the symmetric graph Laplacian, #' a higher value results in more sparsity and faster calculation. #' The predefined value is 10^-5.} #' } #' #' @section Implementation: #' Wraps around \code{\link[diffusionMap]{diffuse}}, see there for #' details. It uses the notation of Richards et al. (2009) which is #' slightly different from the one in the original paper (Coifman and #' Lafon, 2006) and there is no \eqn{\alpha} parameter. #' There is also an out-of-sample extension, see examples. #' #' #' @references #' Richards, J.W., Freeman, P.E., Lee, A.B., Schafer, #' C.M., 2009. Exploiting Low-Dimensional Structure in #' Astronomical Spectra. ApJ 691, #' 32. doi:10.1088/0004-637X/691/1/32 #' #' Coifman, R.R., Lafon, S., 2006. Diffusion maps. Applied and #' Computational Harmonic Analysis 21, #' 5-30. doi:10.1016/j.acha.2006.04.006 #' #' @examples #' dat <- loadDataSet("3D S Curve", n = 300) #' emb <- embed(dat, "DiffusionMaps") #' #' plot(emb, type = "2vars") #' #' # predicting is possible: #' samp <- sample(floor(nrow(dat) / 10)) #' emb2 <- embed(dat[samp]) #' emb3 <- predict(emb2, dat[-samp]) #' #' plot(emb2, type = "2vars") #' points(getData(emb3)) #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export DiffusionMaps #' @exportClass DiffusionMaps DiffusionMaps <- setClass( "DiffusionMaps", contains = "dimRedMethod", prototype = list( stdpars = list(d = stats::dist, ndim = 2, eps = "auto", t = 0, delta = 1e-5), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("diffusionMap") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data distmat <- pars$d(indata) if (pars$eps == "auto") pars$eps <- diffusionMap::epsilonCompute(distmat) diffres <- diffusionMap::diffuse( D = distmat, t = pars$t, eps.val = pars$eps, neigen = pars$ndim, maxdim = pars$ndim, delta = pars$delta ) outdata <- as.matrix(diffres$X) appl <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != ncol(data@data)) stop("x must have the same number of dimensions ", "as the original data") dd <- sqrt(pdist2(proj, indata)) appl.res <- diffusionMap::nystrom(diffres, dd, sigma = diffres$epsilon) dimnames(appl.res) <- list( rownames(x), paste0("diffMap", seq_len(ncol(outdata))) ) new("dimRedData", data = appl.res, meta = appl.meta) } colnames(outdata) <- paste0("diffMap", seq_len(ncol(outdata))) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, apply = appl, has.apply = TRUE, has.org.data = keep.org.data, method = "diffmap", pars = pars )) }) ) dimRed/R/fastica.R0000644000176200001440000000666313562225201013425 0ustar liggesusers#' Independent Component Analysis #' #' An S4 Class implementing the FastICA algorithm for Indepentend #' Component Analysis. #' #' ICA is used for blind signal separation of different sources. It is #' a linear Projection. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' FastICA can take the following parameters: #' \describe{ #' \item{ndim}{The number of output dimensions. Defaults to \code{2}} #' } #' #' @section Implementation: #' Wraps around \code{\link[fastICA]{fastICA}}. FastICA uses a very #' fast approximation for negentropy to estimate statistical #' independences between signals. Because it is a simple #' rotation/projection, forward and backward functions can be given. #' #' @references #' #' Hyvarinen, A., 1999. Fast and robust fixed-point algorithms for independent #' component analysis. IEEE Transactions on Neural Networks 10, 626-634. #' https://doi.org/10.1109/72.761722 #' #' @examples #' dat <- loadDataSet("3D S Curve") #' emb <- embed(dat, "FastICA", ndim = 2) #' plot(getData(getDimRedData(emb))) #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export FastICA #' @exportClass FastICA FastICA <- setClass( "FastICA", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("fastICA") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL orgdata.colmeans <- colMeans(orgdata) indata <- data@data res <- fastICA::fastICA(indata, n.comp = pars$ndim, method = "C") outdata <- res$S colnames(outdata) <- paste0("ICA", 1:ncol(outdata)) appl <- function(x){ appl.meta <- if (inherits(x, "dimRedData")) x@meta else matrix(numeric(0), 0, 0) proj <- if (inherits(x, "dimRedData")) x@data else x out <- scale(proj, center = orgdata.colmeans, scale = FALSE) %*% res$K %*% res$W colnames(out) <- paste0("ICA", 1:ncol(out)) return(new("dimRedData", data = out, meta = appl.meta)) } inv <- function(x){ appl.meta <- if (inherits(x, "dimRedData")) x@meta else matrix(numeric(0), 0, 0) proj <- if (inherits(x, "dimRedData")) x@data else x out <- scale(proj %*% res$A[1:ncol(proj), ], center = -orgdata.colmeans, scale = FALSE) reproj <- new("dimRedData", data = out, meta = appl.meta) return(reproj) } return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, apply = appl, inverse = inv, has.apply = TRUE, has.inverse = TRUE, method = "FastICA", pars = pars )) }) ) dimRed/R/nmds.R0000644000176200001440000000350213562225201012741 0ustar liggesusers#' Non-Metric Dimensional Scaling #' #' An S4 Class implementing Non-Metric Dimensional Scaling. #' #' A non-linear extension of MDS using monotonic regression #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' nMDS can take the following parameters: #' \describe{ #' \item{d}{A distance function.} #' \item{ndim}{The number of embedding dimensions.} #' } #' #' @section Implementation: #' Wraps around the #' \code{\link[vegan]{monoMDS}}. For parameters that are not #' available here, the standard configuration is used. #' #' @references #' #' Kruskal, J.B., 1964. Nonmetric multidimensional scaling: A numerical method. #' Psychometrika 29, 115-129. https://doi.org/10.1007/BF02289694 #' #' @examples #' dat <- loadDataSet("3D S Curve", n = 300) #' emb <- embed(dat, "nMDS") #' plot(emb, type = "2vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export nMDS #' @exportClass nMDS nMDS <- setClass( "nMDS", contains = "dimRedMethod", prototype = list( stdpars = list(d = stats::dist, ndim = 2), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("vegan") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data outdata <- vegan::monoMDS(pars$d(indata), k = pars$ndim)$points colnames(outdata) <- paste0("NMDS", 1:ncol(outdata)) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "nmds", pars = pars )) }) ) dimRed/R/tsne.R0000644000176200001440000000533513562225201012757 0ustar liggesusers#' t-Distributed Stochastic Neighborhood Embedding #' #' An S4 Class for t-SNE. #' #' t-SNE is a method that uses Kullback-Leibler divergence between the #' distance matrices in high and low-dimensional space to embed the #' data. The method is very well suited to visualize complex #' structures in low dimensions. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' t-SNE can take the following parameters: #' \describe{ #' \item{d}{A distance function, defaults to euclidean distances} #' \item{perplexity}{The perplexity parameter, roughly equivalent to neighborhood size.} #' \item{theta}{Approximation for the nearest neighbour search, large values are more inaccurate.} #' \item{ndim}{The number of embedding dimensions.} #' } #' #' @section Implementation: #' #' Wraps around \code{\link[Rtsne]{Rtsne}}, which is very well #' documented. Setting \code{theta = 0} does a normal t-SNE, larger #' values for \code{theta < 1} use the Barnes-Hut algorithm which #' scales much nicer with data size. Larger values for perplexity take #' larger neighborhoods into account. #' #' @references #' Maaten, L. van der, 2014. Accelerating t-SNE using Tree-Based #' Algorithms. Journal of Machine Learning Research 15, 3221-3245. #' #' van der Maaten, L., Hinton, G., 2008. Visualizing Data using #' t-SNE. J. Mach. Learn. Res. 9, 2579-2605. #' #' @examples #' \dontrun{ #' dat <- loadDataSet("3D S Curve", n = 300) #' emb <- embed(dat, "tSNE", perplexity = 80) #' plot(emb, type = "2vars") #' } #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export tSNE #' @exportClass tSNE tSNE <- setClass( "tSNE", contains = "dimRedMethod", prototype = list( stdpars = list(d = stats::dist, perplexity = 30, theta = 0.5, ndim = 2), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("Rtsne") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data outdata <- Rtsne::Rtsne(pars$d(indata), perplexity = pars$perplexity, theta = pars$theta, dims = pars$ndim)$Y colnames(outdata) <- paste0("tSNE", 1:ncol(outdata)) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "tsne", pars = pars )) }) ) dimRed/R/kpca.R0000644000176200001440000001051213562225201012715 0ustar liggesusers#' Kernel PCA #' #' An S4 Class implementing Kernel PCA #' #' Kernel PCA is a nonlinear extension of PCA using kernel methods. #' #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' Kernel PCA can take the following parameters: #' \describe{ #' \item{ndim}{the number of output dimensions, defaults to 2} #' \item{kernel}{The kernel function, either as a function or a #' character vector with the name of the kernel. Defaults to #' \code{"rbfdot"}} #' \item{kpar}{A list with the parameters for the kernel function, #' defaults to \code{list(sigma = 0.1)}} #' } #' #' The most comprehensive collection of kernel functions can be found in #' \code{\link[kernlab]{kpca}}. In case the function does not take any #' parameters \code{kpar} has to be an empty list. #' #' @section Implementation: #' #' Wraps around \code{\link[kernlab]{kpca}}, but provides additionally #' forward and backward projections. #' #' @references #' #' Sch\"olkopf, B., Smola, A., M\"uller, K.-R., 1998. Nonlinear Component Analysis #' as a Kernel Eigenvalue Problem. Neural Computation 10, 1299-1319. #' https://doi.org/10.1162/089976698300017467 #' #' @examples #' \dontrun{ #' dat <- loadDataSet("3D S Curve") #' emb <- embed(dat, "kPCA") #' plot(emb, type = "2vars") #' } #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export kPCA #' @exportClass kPCA kPCA <- setClass( "kPCA", contains = "dimRedMethod", prototype = list( stdpars = list(kernel = "rbfdot", kpar = list(sigma = 0.1), ndim = 2), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("kernlab") if (is.null(pars$ndim)) pars$ndim <- 2 meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data message(Sys.time(), ": Calculating kernel PCA") res <- do.call(kernlab::kpca, c(list(x = indata), pars)) kernel <- get_kernel_fun(pars$kernel, pars$kpar) message(Sys.time(), ": Trying to calculate reverse") K_rev <- kernlab::kernelMatrix(kernel, res@rotated) diag(K_rev) <- 0.1 + diag(K_rev) dual_coef <- try(solve(K_rev, indata), silent = TRUE) appl <- function (x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x proj <- kernlab::predict(res, proj)[, 1:pars$ndim, drop = FALSE] colnames(proj) <- paste0("kPCA", 1:ncol(proj)) new("dimRedData", data = proj, meta = appl.meta) } inv <- if (inherits(dual_coef, "try-error")) { message("No inverse function.") function(x) NA } else { function (x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x resrot <- res@rotated[, 1:ncol(proj)] rot <- kernlab::kernelMatrix(kernel, proj, resrot) proj <- rot %*% dual_coef new("dimRedData", data = proj, meta = appl.meta) } } outdata <- res@rotated[, 1:pars$ndim, drop = FALSE] colnames(outdata) <- paste0("kPCA", 1:ncol(outdata)) message(Sys.time(), ": DONE") return( new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, apply = appl, inverse = inv, has.org.data = keep.org.data, has.apply = TRUE, has.inverse = TRUE, method = "kpca", pars = pars ) ) }) ) ## get the kernel function out of the kernlab namespace: get_kernel_fun <- function (kernel, pars) { if (!is(kernel, "kernel")) { if (is(kernel, "function")) { kernel <- deparse(substitute(kernel)) } else { kernel <- get(kernel, asNamespace("kernlab")) } kernel <- do.call(kernel, pars) } return(kernel) } dimRed/R/autoencoder.R0000644000176200001440000003635514153211745014331 0ustar liggesusers#' AutoEncoder #' #' An S4 Class implementing an Autoencoder #' #' Autoencoders are neural networks that try to reproduce their input. Consider #' this method unstable, as the internals may still be changed. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' Autoencoder can take the following parameters: #' \describe{ #' \item{ndim}{The number of dimensions for reduction.} #' \item{n_hidden}{The number of neurons in the hidden #' layers, the length specifies the number of layers, #' the length must be impair, the middle number must #' be the same as ndim.} #' \item{activation}{The activation functions for the layers, #' one of "tanh", "sigmoid", "relu", "elu", everything #' else will silently be ignored and there will be no #' activation function for the layer.} #' \item{weight_decay}{the coefficient for weight decay, #' set to 0 if no weight decay desired.} #' \item{learning_rate}{The learning rate for gradient descend} #' \item{graph}{Optional: A list of bits and pieces that define the #' autoencoder in tensorflow, see details.} #' \item{keras_graph}{Optional: A list of keras layers that define #' the encoder and decoder, specifying this, will ignore all #' other topology related variables, see details.} #' \item{batchsize}{If NA, all data will be used for training, #' else only a random subset of size batchsize will be used} #' \item{n_steps}{the number of training steps.} #' } #' #' @section Details: #' There are several ways to specify an autoencoder, the simplest is to pass the #' number of neurons per layer in \code{n_hidden}, this must be a vector of #' integers of impair length and it must be symmetric and the middle number must #' be equal to \code{ndim}, For every layer an activation function can be #' specified with \code{activation}. #' #' For regularization weight decay can be specified by setting #' \code{weight_decay} > 0. #' #' Currently only a gradient descent optimizer is used, the learning rate can be #' specified by setting \code{learning_rate}. #' The learner can operate on batches if \code{batchsize} is not \code{NA}. #' The number of steps the learner uses is specified using \code{n_steps}. #' #' @section Further training a model: #' If the model did not converge in the first training phase or training with #' different data is desired, the \code{\link{dimRedResult}} object may be #' passed as \code{autoencoder} parameter; In this case all topology related #' parameters will be ignored. #' #' @section Using Keras layers: #' The encoder and decoder part can be specified using a list of \pkg{keras} #' layers. This requires a list with two entries, \code{encoder} should contain #' a LIST of keras layers WITHOUT the \code{\link[keras]{layer_input}} #' that will be concatenated in order to form the encoder part. #' \code{decoder} should be #' defined accordingly, the output of \code{decoder} must have the same number #' of dimensions as the input data. #' #' @section Using Tensorflow: #' The model can be entirely defined in \pkg{tensorflow}, it must contain a #' list with the following entries: #' \describe{ #' \item{encoder}{A tensor that defines the encoder.} #' \item{decoder}{A tensor that defines the decoder.} #' \item{network}{A tensor that defines the reconstruction (encoder + decoder).} #' \item{loss}{A tensor that calculates the loss (network + loss function).} #' \item{in_data}{A \code{placeholder} that points to the data input of #' the network AND the encoder.} #' \item{in_decoder}{A \code{placeholder} that points to the input of #' the decoder.} #' \item{session}{A \pkg{tensorflow} \code{Session} object that holds #' the values of the tensors.} #' } #' #' @section Implementation: #' Uses \pkg{tensorflow} as a backend, for details an #' problems relating tensorflow, see \url{https://tensorflow.rstudio.com}. #' #' @examples #' \dontrun{ #' dat <- loadDataSet("3D S Curve") #' #' emb <- embed(dat, "AutoEncoder") #' #' # predicting is possible: #' samp <- sample(floor(nrow(dat) / 10)) #' emb2 <- embed(dat[samp]) #' emb3 <- predict(emb2, dat[-samp]) #' #' plot(emb, type = "2vars") #' plot(emb2, type = "2vars") #' points(getData(emb3)) #' } #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export AutoEncoder #' @exportClass AutoEncoder AutoEncoder <- setClass( "AutoEncoder", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, n_hidden = c(10, 2, 10), activation = c("tanh", "lin", "tanh"), weight_decay = 0.001, learning_rate = 0.15, graph = NULL, keras_graph = NULL, ## is.na() of an S4 class gives a warning autoencoder = NULL, batchsize = NA, n_steps = 500), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("tensorflow") tensorflow::tf$compat$v1$disable_v2_behavior() meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data graph <- if (!is.null(pars$graph)) { message("using predefined graph, ", "ignoring other parameters that define topology, ", "be sure to set ndim to the correct value ", "else you might run into trouble.") pars$graph } else if (!is.null(pars$autoencoder)) { message("using predefined autoencoder object, ", " ignoring other parameters that define topology.") if (!(inherits(pars$autoencoder, "dimRedResult") && pars$autoencoder@method == "AutoEncoder")) stop("autoencoder must be NULL, ", "or of type dimRedResult by an AutoEncoder object.") ## setting topology related parameters from autoencoder pars$ndim <- pars$autoencoder@pars$ndim pars$n_hidden <- pars$autoencoder@pars$n_hidden pars$activation <- pars$autoencoder@pars$activation pars$autoencoder@pars$graph } else if (!is.null(pars$keras_graph)) { message("using predefined keras graph, ", "ignoring parameters that define topology") tmp <- graph_keras(encoder = pars$keras_graph$encoder, decoder = pars$keras_graph$decoder, n_in = ncol(indata)) pars$ndim <- tmp$encoder$shape$dims[[2]]$value tmp } else { with(pars, { graph_params( d_in = ncol(indata), n_hidden = n_hidden, activation = activation, weight_decay = weight_decay, learning_rate = learning_rate, n_steps = n_steps, ndim = ndim ) }) } if (!"encoder" %in% names(graph)) stop("no encoder in graph") if (!"decoder" %in% names(graph)) stop("no decoder in graph") if (!"network" %in% names(graph)) stop("no network in graph") if (!"loss" %in% names(graph)) stop("no loss in graph") if (!"in_decoder" %in% names(graph)) stop("no in_decoder in graph") if (!"in_data" %in% names(graph)) stop("no in_data in graph") if (!"session" %in% names(graph)) stop("no session in graph") ## TODO: I am not sure if there is a way to do this directly on the list ## objects graph_data_input <- graph$in_data graph_decoder_input <- graph$in_dec sess <- graph$session optimizer <- tensorflow::tf$compat$v1$train$GradientDescentOptimizer(pars$learning_rate) train <- optimizer$minimize(graph$loss) ## TODO: do proper batching and hold out for (step in 1:pars$n_steps) { sess$run(train, feed_dict = tensorflow::dict( graph_data_input = if (is.na(pars$batchsize)) { indata } else { indata[ sample(seq_len(nrow(indata)), pars$batchsize), ] } ) ) } outdata <- sess$run(graph$encoder, feed_dict = tensorflow::dict(graph_data_input = indata)) appl <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != ncol(data@data)) stop("x must have the same number of dimensions ", "as the original data") res <- sess$run(graph$encoder, feed_dict = tensorflow::dict(graph_data_input = proj)) colnames(res) <- paste0("AE", seq_len(ncol(res))) new("dimRedData", data = res, meta = appl.meta) } inv <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != pars$ndim) stop("x must have the same number of dimensions ", "as ndim data") res <- sess$run( graph$decoder, feed_dict = tensorflow::dict( graph_decoder_input = proj )) colnames(res) <- colnames(indata) new("dimRedData", data = res, meta = appl.meta) } ## TODO: this is a hack and there should be an "official" way to save ## extra data in a dimRedResult object pars$graph <- graph colnames(outdata) <- paste0("AE", seq_len(ncol(outdata))) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, apply = appl, inverse = inv, has.apply = TRUE, has.inverse = TRUE, has.org.data = keep.org.data, method = "AutoEncoder", pars = pars )) }) ) get_activation_function <- function(x) { switch( x, tanh = tensorflow::tf$compat$v1$tanh, sigmoid = tensorflow::tf$compat$v1$sigmoid, relu = tensorflow::tf$compat$v1$nn$relu, elu = tensorflow::tf$compat$v1$elu, I ) } ## no idea why these and variants do not work: ## chain_list <- function(x1, x2) Reduce(`%>%`, x2, init = x1) ## chain_list <- function(x) Reduce(`%>%`, x) chain_list <- function (x1, x2 = NULL) { if(is.null(x2)) { stopifnot(is.list(x1)) result <- x1[[1]] if(length(x1) > 1) for (i in 2:length(x1)) { result <- result %>% (x1[[i]]) } } else { stopifnot(is.list(x2)) result <- x1 for (i in 1:length(x2)) { result <- result %>% (x2[[i]]) } } return(result) } graph_keras <- function(encoder, decoder, n_in) { chckpkg("keras") chckpkg("tensorflow") inenc <- keras::layer_input(shape = n_in) enc <- inenc %>% chain_list(encoder) ndim <- enc$shape$dims[[2]]$value indec <- keras::layer_input(shape = ndim) dec <- indec %>% chain_list(decoder) encdec <- inenc %>% chain_list(encoder) %>% chain_list(decoder) ## TODO: check if this uses weight decay, probably not: loss <- tensorflow::tf$compat$v1$reduce_mean((encdec - inenc) ^ 2) sess <- tensorflow::tf$compat$v1$keras$backend$get_session() return(list( encoder = enc, decoder = dec, network = encdec, loss = loss, in_data = inenc, in_decoder = indec, session = sess )) } graph_params <- function ( d_in, n_hidden, activation, weight_decay, learning_rate, n_steps, ndim ) { if (length(n_hidden) %% 2 == 0) stop("the number of layers must be impair") if (ndim != n_hidden[ceiling(length(n_hidden) / 2)]) stop("the middle of n_hidden must be equal to ndim") if (length(n_hidden) != length(activation)) stop("declare an activation function for each layer:", "\nn_hidden: ", paste(n_hidden, collapse = " "), "\nactivation functions: ", paste(activation, collapse = " ")) if (weight_decay < 0) stop("weight decay must be > 0") if (learning_rate <= 0) stop("learning rate must be > 0") if (n_steps <= 0) stop("n_steps must be > 0") input <- tensorflow::tf$compat$v1$placeholder( "float", shape = tensorflow::shape(NULL, d_in), name = "input" ) indec <- tensorflow::tf$compat$v1$placeholder( "float", shape = tensorflow::shape(NULL, ndim), name = "nlpca" ) w <- lapply(seq_len(length(n_hidden) + 1), function(x) { n1 <- if (x == 1) d_in else n_hidden[x - 1] n2 <- if (x > length(n_hidden)) d_in else n_hidden[x] tensorflow::tf$compat$v1$Variable(tensorflow::tf$compat$v1$random_uniform(tensorflow::shape(n1, n2), 1.0, -1.0), name = paste0("w_", x)) }) b <- lapply(seq_len(length(n_hidden) + 1), function (x) { n <- if (x > length(n_hidden)) d_in else n_hidden[x] tensorflow::tf$compat$v1$Variable(tensorflow::tf$compat$v1$zeros(tensorflow::shape(n)), name = paste0("b_", x)) }) enc <- input for (i in 1:ceiling(length(n_hidden) / 2)) { sigma <- get_activation_function(activation[i]) enc <- sigma(tensorflow::tf$compat$v1$matmul(enc, w[[i]]) + b[[i]]) } dec <- indec for (i in (ceiling(length(n_hidden) / 2) + 1):(length(n_hidden) + 1)) { sigma <- get_activation_function(activation[i]) dec <- sigma(tensorflow::tf$compat$v1$matmul(dec, w[[i]]) + b[[i]]) } encdec <- enc for (i in (ceiling(length(n_hidden) / 2) + 1):(length(n_hidden) + 1)) { sigma <- get_activation_function(activation[i]) encdec <- sigma(tensorflow::tf$compat$v1$matmul(encdec, w[[i]]) + b[[i]]) } loss <- Reduce(`+`, lapply(w, function (x) tensorflow::tf$compat$v1$reduce_sum(tensorflow::tf$compat$v1$pow(x, 2))), 0) loss <- Reduce(`+`, lapply(b, function (x) tensorflow::tf$compat$v1$reduce_sum(tensorflow::tf$compat$v1$pow(x, 2))), loss) loss <- tensorflow::tf$compat$v1$reduce_mean((encdec - input) ^ 2) + weight_decay * loss sess <- tensorflow::tf$compat$v1$Session() ## This closes sess if it is garbage collected. reg.finalizer(sess, function(x) x$close()) sess$run(tensorflow::tf$compat$v1$global_variables_initializer()) return(list( encoder = enc, decoder = dec, network = encdec, loss = loss, in_data = input, in_decoder = indec, session = sess )) } dimRed/R/isomap.R0000644000176200001440000002024413562225201013272 0ustar liggesusers#' Isomap embedding #' #' An S4 Class implementing the Isomap Algorithm #' #' The Isomap algorithm approximates a manifold using geodesic #' distances on a k nearest neighbor graph. Then classical scaling is #' performed on the resulting distance matrix. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' Isomap can take the following parameters: #' \describe{ #' \item{knn}{The number of nearest neighbors in the graph. Defaults to 50.} #' \item{ndim}{The number of embedding dimensions, defaults to 2.} #' \item{get_geod}{Should the geodesic distance matrix be kept, #' if \code{TRUE}, access it as \code{getOtherData(x)$geod}} #' } #' #' @section Implementation: #' #' The dimRed package uses its own implementation of Isomap which also #' comes with an out of sample extension (known as landmark #' Isomap). The default Isomap algorithm scales computationally not #' very well, the implementation here uses \code{\link[RANN]{nn2}} for #' a faster search of the nearest neighbors. If data are too large it #' may be useful to fit a subsample of the data and use the #' out-of-sample extension for the other points. #' #' @references #' Tenenbaum, J.B., Silva, V. de, Langford, J.C., 2000. A Global Geometric #' Framework for Nonlinear Dimensionality Reduction. Science 290, 2319-2323. #' https://doi.org/10.1126/science.290.5500.2319 #' #' @examples #' dat <- loadDataSet("3D S Curve", n = 500) #' emb <- embed(dat, "Isomap", knn = 10) #' plot(emb) #' #' ## or simpler, use embed(): #' samp <- sample(nrow(dat), size = 200) #' emb2 <- embed(dat[samp], "Isomap", .mute = NULL, knn = 10) #' emb3 <- predict(emb2, dat[-samp]) #' #' plot(emb2, type = "2vars") #' plot(emb3, type = "2vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export Isomap #' @exportClass Isomap Isomap <- setClass( "Isomap", contains = "dimRedMethod", prototype = list( stdpars = list(knn = 50, ndim = 2, get_geod = FALSE), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("RSpectra") chckpkg("igraph") chckpkg("RANN") message(Sys.time(), ": Isomap START") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data if (is.null(pars$eps)) pars$eps <- 0 if (is.null(pars$get_geod)) pars$get_geod <- FALSE ## geodesic distances message(Sys.time(), ": constructing knn graph") knng <- makeKNNgraph(x = indata, k = pars$knn, eps = pars$eps) message(Sys.time(), ": calculating geodesic distances") geodist <- igraph::distances(knng, algorithm = "dijkstra") message(Sys.time(), ": Classical Scaling") ## TODO: add regularization k <- geodist ^ 2 k <- .Call(stats:::C_DoubleCentre, k) k <- - k / 2 ## TODO: explicit symmetrizing ## TODO: return eigenvectors? e <- RSpectra::eigs_sym(k, pars$ndim, which = "LA", opts = list(retvec = TRUE)) e_values <- e$values e_vectors <- e$vectors neig <- sum(e_values > 0) if (neig < pars$ndim) { warning("Isomap: eigenvalues < 0, returning less dimensions!") e_values <- e_values[seq_len(neig)] e_vectors <- e_vectors[, seq_len(neig), drop = FALSE] } e_vectors <- e_vectors * rep(sqrt(e_values), each = nrow(e_vectors)) colnames(e_vectors) <- paste("iso", seq_len(neig)) appl <- function (x) { message(Sys.time(), ": L-Isomap embed START") appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() indata <- if (inherits(x, "dimRedData")) x@data else x if (ncol(indata) != ncol(data@data)) stop("x must have the same number of dimensions as the original data") nindata <- nrow(indata) norg <- nrow(orgdata) message(Sys.time(), ": constructing knn graph") lknng <- makeKNNgraph(rbind(indata, orgdata), k = pars$knn, eps = pars$eps) message(Sys.time(), ": calculating geodesic distances") lgeodist <- igraph::distances(lknng, seq_len(nindata), nindata + seq_len(norg)) message(Sys.time(), ": embedding") dammu <- sweep(lgeodist ^ 2, 2, colMeans(geodist ^ 2), "-") Lsharp <- sweep(e_vectors, 2, e_values, "/") out <- -0.5 * (dammu %*% Lsharp) message(Sys.time(), ": DONE") return(new("dimRedData", data = out, meta = appl.meta)) } return(new( "dimRedResult", data = new("dimRedData", data = e_vectors, meta = meta), org.data = orgdata, has.org.data = keep.org.data, apply = appl, has.apply = TRUE, method = "Isomap", pars = pars, other.data = if (pars$get_geod) list(geod = as.dist(geodist)) else list() )) }) ) ## input data(matrix or data frame) return knn graph implements ## "smart" choices on RANN::nn2 parameters we ignore radius search ## TODO: find out a good limit to switch from kd to bd trees COMMENT: ## bd trees are buggy, they dont work if there are duplicated data ## points and checking would neutralize the performance gain, so bd ## trees are not really usable. makeKNNgraph <- function (x, k, eps = 0, diag = FALSE){ ## requireNamespace("RANN") ## requireNamespace("igraph") ## consts INF_VAL <- 1.340781e+15 NA_IDX <- 0 BDKD_LIM <- 1000000 #todo: figure out a good value here ## select parameters M <- nrow(x) treetype <- "kd" # if (M < BDKD_LIM) "kd" else "bd" # see: # https://github.com/jefferis/RANN/issues/19 searchtype <- if (eps == 0) "standard" else "priority" ## RANN::nn2 returns the points in data with respect to query ## e.g. the rows in the output are the points in query and the ## columns the points in data. nn2res <- RANN::nn2(data = x, query = x, k = k + 1, treetype = treetype, searchtype = searchtype, eps = eps) ## create graph: the first ny nodes will be y, the last nx nodes ## will be x, if x != y ## it is not really pretty to create a ## directed graph first and then make it undirected. g <- igraph::make_empty_graph(M, directed = TRUE) g[from = if (diag) rep(seq_len(M), times = k + 1) else rep(seq_len(M), times = k), to = if (diag) as.vector(nn2res$nn.idx) else as.vector(nn2res$nn.idx[, -1]), attr = "weight"] <- if (diag) as.vector(nn2res$nn.dists) else as.vector(nn2res$nn.dists[, -1]) return(igraph::as.undirected(g, mode = "collapse", edge.attr.comb = "first")) } ## the original isomap method I'll keep it here for completeness: ## isomap <- new("dimRedMethod", ## stdpars = list(knn = 50, ## d = dist, ## ndim = 2) ## fun = function (data, pars, ## keep.org.data = TRUE) { ## chckpkg("vegan") ## meta <- data@meta ## orgdata <- if (keep.org.data) data@data else NULL ## indata <- data@data ## outdata <- vegan::isomap(pars$d(indata), ## ndim = pars$ndim, ## k = pars$knn)$points ## colnames(outdata) <- paste0("Iso", 1:ncol(outdata)) ## return(new( ## "dimRedResult", ## data = new("dimRedData", ## data = outdata, ## meta = meta), ## org.data = orgdata, ## has.org.data = keep.org.data, ## method = "isomap", ## pars = pars ## )) ## }) dimRed/R/umap.R0000644000176200001440000001064414153200510012740 0ustar liggesusers#' Umap embedding #' #' An S4 Class implementing the UMAP algorithm #' #' Uniform Manifold Approximation is a gradient descend based algorithm that #' gives results similar to t-SNE, but scales better with the number of points. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' #' UMAP can take the follwing parameters: #' \describe{ #' \item{ndim}{The number of embedding dimensions.} #' \item{knn}{The number of neighbors to be used.} #' \item{d}{The distance metric to use.} #' \item{method}{\code{"naive"} for an R implementation, \code{"python"} #' for the reference implementation.} #' } #' #' Other method parameters can also be passed, see #' \code{\link[umap]{umap.defaults}} for details. The ones above have been #' standardized for the use with \code{dimRed} and will get automatically #' translated for \code{\link[umap]{umap}}. #' #' @section Implementation: #' #' The dimRed package wraps the \code{\link[umap]{umap}} packages which provides #' an implementation in pure R and also a wrapper around the original python #' package \code{umap-learn} (https://github.com/lmcinnes/umap/). This requires #' \code{umap-learn} version 0.4 installed, at the time of writing, there is #' already \code{umap-learn} 0.5 but it is not supported by the R package #' \code{\link[umap]{umap}}. #' #' The \code{"naive"} implementation is a pure R implementation and considered #' experimental at the point of writing this, it is also much slower than the #' python implementation. #' #' The \code{"python"} implementation is the reference implementation used by #' McInees et. al. (2018). It requires the \code{\link[reticulate]{reticulate}} #' package for the interaction with python and the python package #' \code{umap-learn} installed (use \code{pip install umap-learn}). #' #' @references #' #' McInnes, Leland, and John Healy. #' "UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction." #' https://arxiv.org/abs/1802.03426 #' #' @examples #' \dontrun{ #' dat <- loadDataSet("3D S Curve", n = 300) #' emb <- embed(dat, "UMAP", .mute = NULL, knn = 10) #' plot(emb, type = "2vars") #' } #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export UMAP #' @exportClass UMAP UMAP <- setClass( "UMAP", contains = "dimRedMethod", prototype = list( stdpars = list( knn = 15, ndim = 2, d = "euclidean", method = "umap-learn" ), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("umap") if (pars$method == "python") { chckpkg("reticulate") if (!reticulate::py_module_available("umap")) stop("cannot find python umap, install with `pip install umap-learn`") } meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data ## Create config umap_call_pars <- umap::umap.defaults umap_call_pars$n_neighbors <- pars$knn umap_call_pars$n_components <- pars$ndim umap_call_pars$metric <- pars$d umap_call_pars$method <- pars$method umap_call_pars$d <- indata pars_2 <- pars pars_2$knn <- NULL pars_2$ndim <- NULL pars_2$d <- NULL pars_2$method <- NULL for (n in names(pars_2)) umap_call_pars[[n]] <- pars_2[[n]] ## Do the embedding outdata <- do.call(umap::umap, umap_call_pars) ## Post processing colnames(outdata$layout) <- paste0("UMAP", 1:ncol(outdata$layout)) appl <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != ncol(orgdata)) stop("x must have the same number of dimensions ", "as the original data") new_proj <- umap:::predict.umap(outdata, as.matrix(proj)) colnames(new_proj) <- paste0("UMAP", 1:ncol(new_proj)) rownames(new_proj) <- NULL out_data <- new("dimRedData", data = new_proj, meta = appl.meta) return(out_data) } return(new( "dimRedResult", data = new("dimRedData", data = outdata$layout, meta = meta), org.data = orgdata, apply = appl, has.org.data = keep.org.data, has.apply = TRUE, method = "UMAP", pars = pars )) } ) ) dimRed/R/mds.R0000644000176200001440000001150013562741725012576 0ustar liggesusers#' Metric Dimensional Scaling #' #' An S4 Class implementing classical scaling (MDS). #' #' MDS tries to maintain distances in high- and low-dimensional space, #' it has the advantage over PCA that arbitrary distance functions can #' be used, but it is computationally more demanding. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' MDS can take the following parameters: #' \describe{ #' \item{ndim}{The number of dimensions.} #' \item{d}{The function to calculate the distance matrix from the input coordinates, defaults to euclidean distances.} #' } #' #' @section Implementation: #' #' Wraps around \code{\link[stats]{cmdscale}}. The implementation also #' provides an out-of-sample extension which is not completely #' optimized yet. #' #' @references #' #' Torgerson, W.S., 1952. Multidimensional scaling: I. Theory and method. #' Psychometrika 17, 401-419. https://doi.org/10.1007/BF02288916 #' #' @examples #' \dontrun{ #' dat <- loadDataSet("3D S Curve") #' emb <- embed(dat, "MDS") #' plot(emb, type = "2vars") #' #' # a "manual" kPCA: #' emb2 <- embed(dat, "MDS", d = function(x) exp(stats::dist(x))) #' plot(emb2, type = "2vars") #' #' # a "manual", more customizable, and slower Isomap: #' emb3 <- embed(dat, "MDS", d = function(x) vegan::isomapdist(vegan::vegdist(x, "manhattan"), k = 20)) #' plot(emb3) #' #' } #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export MDS #' @exportClass MDS MDS <- setClass( "MDS", contains = "dimRedMethod", prototype = list( stdpars = list(d = stats::dist, ndim = 2), fun = function (data, pars, keep.org.data = TRUE) { ## meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data ## there are only efficient implementations for euclidean ## distances: extra efficient implementation for euclidean ## distances are possible, D is quared several times, it would be ## much faster to compute the squared distance right away. has.apply <- identical(all.equal(pars$d, dist), TRUE) # == TRUE # necessary, # because # all.equal # returns # TRUE or an # error # string!!!! D <- as.matrix(pars$d(indata)) if (has.apply) mD2 <- mean(D ^ 2) ## cmdscale square the matrix internally res <- stats::cmdscale(D, k = pars$ndim) outdata <- res D <- NULL ## Untested: remove that from environment before creating ## appl function, else it will stay in its environment ## forever appl <- if (!has.apply) function(x) NA else function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x ## double center new data with respect to old: TODO: optimize ## this method, according to the de Silva, Tenenbaum(2004) ## paper. Need an efficient method to calculate the distance ## matrices between different point sets and arbitrary ## distances. Kab <- as.matrix(pars$d(proj) ^ 2) Exa <- colMeans(pdist2(indata, proj)) Kab <- sweep(Kab, 1, Exa) #, "-") Kab <- sweep(Kab, 2, Exa) #, "-") Kab <- -0.5 * (Kab + mD2) ## Eigenvalue decomposition tmp <- eigen(Kab, symmetric = TRUE) ev <- tmp$values[seq_len(pars$ndim)] evec <- tmp$vectors[, seq_len(pars$ndim), drop = FALSE] k1 <- sum(ev > 0) if (k1 < pars$ndim) { warning(gettextf("only %d of the first %d eigenvalues are > 0", k1, k), domain = NA) evec <- evec[, ev > 0, drop = FALSE] ev <- ev[ev > 0] } points <- evec * rep(sqrt(ev), each = nrow(proj)) dimnames(points) <- list(NULL, paste0("MDS", seq_len(ncol(points)))) new("dimRedData", data = points, meta = appl.meta) } colnames(outdata) <- paste0("MDS", seq_len(ncol(outdata))) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, apply = appl, has.org.data = keep.org.data, has.apply = has.apply, method = "mds", pars = pars )) }) ) dimRed/R/dimRedMethod-class.R0000644000176200001440000000650213371631672015466 0ustar liggesusers#' Class "dimRedMethod" #' #' A virtual class "dimRedMethod" to serve as a template to implement #' methods for dimensionality reduction. #' #' Implementations of dimensionality reductions should inherit from #' this class. #' #' The \code{fun} slot should be a function that takes three arguments #' \describe{ #' \item{data}{An object of class \code{\link{dimRedData}}.} #' \item{pars}{A list with the standard parameters.} #' \item{keep.org.data}{Logical. If the original data should be kept in the output.} #' } #' and returns an object of class \code{\link{dimRedResult}}. #' #' The \code{stdpars} slot should take a list that contains standard #' parameters for the implemented methods. #' #' This way the method can be called by \code{embed(data, "method-name", #' ...)}, where \code{...} can be used to to change single parameters. #' #' #' @slot fun A function that does the embedding. #' @slot stdpars A list with the default parameters for the \code{fun} #' slot. #' #' @family dimensionality reduction methods #' @export setClass("dimRedMethod", contains = "VIRTUAL", slots = c(fun = "function", stdpars = "list")) #' dimRedMethodList #' #' Get the names of all methods for dimensionality reduction. #' #' Returns the name of all classes that inherit from #' \code{\link{dimRedMethod-class}} to use with \code{\link{embed}}. #' #' @return a character vector with the names of classes that inherit #' from \code{dimRedMethod}. #' #' @examples #' dimRedMethodList() #' #' @family dimensionality reduction methods #' @export dimRedMethodList <- function () { ## return(c( ## "graph_kk", ## "graph_drl", ## "graph_fr", ## "drr", ## "isomap", ## "diffmap", ## "tsne", ## "nmds", ## "mds", ## "ica", ## "pca", ## "lle", ## ## those two methods are buggy and can produce segfaults: ## ## "loe", "soe", ## "leim", ## "kpca" ## )) names(completeClassDefinition("dimRedMethod", doExtends = FALSE)@subclasses) } # to put standard values for omitted arguments setGeneric("matchPars", function(object, pars) standardGeneric("matchPars"), valueClass = c("list")) setMethod("matchPars", signature(object = "dimRedMethod", pars = "list"), definition = function(object, pars) { nsp <- names(object@stdpars) ncp <- names(pars) nap <- union(nsp, ncp) res <- list() ## exists can deal with elements being NULL ## to assign list@el <- NULL do: ## list["el"] <- list(NULL) for (np in nap) { miss.std <- !exists(np, where = object@stdpars) miss.par <- !exists(np, where = pars) if (miss.std) { warning("Parameter matching: ", np, " is not a standard parameter, ignoring.") } else if (miss.par) { res[np] <- object@stdpars[np] } else { res[np] <- pars[np] } } ## if the method does not accept parameters we have to return ## null, so in embed there is no args$par created. and passed by ## do.call in the embed() function. if (length(res) != 0) ## return(res) else return(NULL) ## first try without the above, all methods should have a pars ## argument. return(res) }) dimRed/R/mixColorSpaces.R0000644000176200001440000000452313354441317014746 0ustar liggesusers#' Mixing color ramps #' #' mix different color ramps #' #' automatically create colors to represent a varying number of #' dimensions. #' #' @param vars a list of variables #' @param ramps a list of color ramps, one for each variable. #' #' @examples #' cols <- expand.grid(x = seq(0, 1, length.out = 10), #' y = seq(0, 1, length.out = 10), #' z = seq(0, 1, length.out = 10)) #' mixed <- mixColor3Ramps(cols) #' #' \dontrun{ #' library(rgl) #' plot3d(cols$x, cols$y, cols$z, col = mixed, pch = 15) #' #' cols <- expand.grid(x = seq(0, 1, length.out = 10), #' y = seq(0, 1, length.out = 10)) #' mixed <- mixColor2Ramps(cols) #' } #' #' plot(cols$x, cols$y, col = mixed, pch = 15) #' @importFrom grDevices colorRamp #' @importFrom grDevices rgb #' @export mixColorRamps <- function (vars, ramps) { if (length(vars) > length(ramps)) stop("need more or equal ramps than vars") nvars <- length(vars) rgbs <- list() for (i in 1:nvars){ rgbs[[i]] <- ramps[[i]](scale01(as.numeric(vars[[i]]))) } retrgb <- Reduce(`+`, rgbs) res <- apply(retrgb, 2, function(x) (x - min(x)) / (max(x) - min(x))) res[is.nan(res)] <- 0 return(rgb(res)) } #' @rdname mixColorRamps #' @export mixColor1Ramps <- function (vars, ramps = colorRamp(c("blue", "black", "red"))) { mixColorRamps(vars, list(ramps)) } #' @rdname mixColorRamps #' @export mixColor2Ramps <- function (vars, ramps = list(colorRamp(c("blue", "green")), colorRamp(c("blue", "red")))) { mixColorRamps(vars, ramps) } #' @rdname mixColorRamps #' @export mixColor3Ramps <- function (vars, ramps = list(colorRamp(c("#001A00", "#00E600")), colorRamp(c("#00001A", "#0000E6")), colorRamp(c("#1A0000", "#E60000")))) { mixColorRamps(vars, ramps) } colorize <- function (vars) { l <- length(vars) if (l == 1) return(mixColor1Ramps(vars)) if (l == 2) return(mixColor2Ramps(vars)) if (l == 3) return(mixColor3Ramps(vars)) return("#000000") } scale01 <- function(x, low = min(x, na.rm = TRUE), high = max(x, na.rm = FALSE)) { x <- (x - low) / (high - low) x } dimRed/R/get_info.R0000644000176200001440000000205413562225201013573 0ustar liggesusers#' getRotationMatrix #' #' Extract the rotation matrix from \code{\link{dimRedResult}} objects derived from PCA and FastICA #' #' The data has to be pre-processed the same way as the method does, e.g. #' centering and/or scaling. #' #' @param x of type \code{\link{dimRedResult}} #' @return a matrix #' #' @examples #' dat <- loadDataSet("Iris") #' #' pca <- embed(dat, "PCA") #' ica <- embed(dat, "FastICA") #' #' rot_pca <- getRotationMatrix(pca) #' rot_ica <- getRotationMatrix(ica) #' #' scale(getData(dat), TRUE, FALSE) %*% rot_pca - getData(getDimRedData(pca)) #' scale(getData(dat), TRUE, FALSE) %*% rot_ica - getData(getDimRedData(ica)) #' #' @family convenience functions #' @export getRotationMatrix <- function(x) { if(!inherits(x, "dimRedResult")) stop("x must be of type 'dimRedResult'") if(x@method == "PCA") return(environment(x@apply)$rot) if(x@method == "PCA_L1") return(environment(x@apply)$rot) if(x@method == "FastICA") return(environment(x@apply)$res$K %*% environment(x@apply)$res$W) stop(paste("Not implemented for", x@method)) } dimRed/R/l1pca.R0000644000176200001440000001402613562225201013003 0ustar liggesusers#' Principal Component Analysis with L1 error. #' #' S4 Class implementing PCA with L1 error. #' #' PCA transforms the data so that the L2 reconstruction error is minimized or #' the variance of the projected data is maximized. This is sensitive to #' outliers, L1 PCA minimizes the L1 reconstruction error or maximizes the sum #' of the L1 norm of the projected observations. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' PCA can take the following parameters: #' \describe{ #' \item{ndim}{The number of output dimensions.} #' \item{center}{logical, should the data be centered, defaults to \code{TRUE}.} #' \item{scale.}{logical, should the data be scaled, defaults to \code{FALSE}.} #' \item{fun}{character or function, the method to apply, see the \code{pcaL1} package} #' \item{\ldots}{other parameters for \code{fun}} #' } #' #' @section Implementation: #' #' Wraps around the different methods is the \code{pcaL1} package. Because PCA #' can be reduced to a simple rotation, forward and backward projection #' functions are supplied. #' #' @references #' #' Park, Y.W., Klabjan, D., 2016. Iteratively Reweighted Least Squares #' Algorithms for L1-Norm Principal Component Analysis, in: Data Mining (ICDM), #' 2016 IEEE 16th International Conference On. IEEE, pp. 430-438. #' #' @examples #' if(requireNamespace("pcaL1", quietly = TRUE)) { #' dat <- loadDataSet("Iris") #' emb <- embed(dat, "PCA_L1") #' #' plot(emb, type = "2vars") #' plot(inverse(emb, getData(getDimRedData((emb)))), type = "3vars") #' } #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export PCA_L1 #' @exportClass PCA_L1 PCA_L1 <- setClass( "PCA_L1", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, center = TRUE, scale. = FALSE, fun = "awl1pca", projections = "l1"), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("pcaL1") ndim <- pars$ndim orgnames <- colnames(data@data) newnames <- paste0("PC", seq_len(ndim)) meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL data <- data@data fun2 <- if(!is.function(pars$fun)) { get(pars$fun, asNamespace("pcaL1")) } else { pars$fun } ce <- if (is.numeric(pars$center)) { if (length(pars$center) != dim(data)[2]) error("center must be logical or have the same length as the data dimensions") pars$center } else if (is.logical(pars$center)) { if (pars$center) colMeans(data) else FALSE } sc <- if (is.numeric(pars$scale.)) { if (length(pars$scale.) != dim(data)[2]) stop("center must be logical or have the same length as the data dimensions") pars$scale. } else if (is.logical(pars$scale.)) { if (pars$scale.) apply(data, 2, sd) else FALSE } if(!(pars$center == FALSE && pars$scale. == FALSE)) data <- scale(data, ce, sc) pars$center <- NULL pars$scale. <- NULL pars$ndim <- NULL pars$fun <- NULL res <- do.call( fun2, c(list(X = data, projDim = ndim, center = FALSE), pars) ) ## evaluate results here for functions data <- res$scores colnames(data) <- paste0("PC", seq_len(ndim)) rot <- res$loadings[, seq_len(ndim), drop = FALSE] dimnames(rot) <- list(orgnames, newnames) rerot <- t(rot) appl <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != ncol(orgdata)) stop("x must have the same number of dimensions ", "as the original data") if (ce[1] != FALSE) proj <- t(apply(proj, 1, function(x) x - ce)) if (sc[1] != FALSE) proj <- t(apply(proj, 1, function(x) x / sc)) proj <- if (pars$projections == "l1") { tmp <- pcaL1::l1projection(proj, rot)$scores colnames(tmp) <- paste0("PC", seq_len(ndim)) tmp } else if (pars$projections == "l2") { proj %*% rot } else { stop("projections must be eiter 'l1' or 'l2'") } proj <- new("dimRedData", data = proj, meta = appl.meta) return(proj) } inv <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) > ncol(data)) stop("x must have less or equal number of dimensions ", "as the original data") d <- ncol(proj) reproj <- proj %*% rerot[seq_len(d), ] if (sc[1] != FALSE) reproj <- t(apply(reproj, 1, function(x) x * sc)) if (ce[1] != FALSE) reproj <- t(apply(reproj, 1, function(x) x + ce)) colnames(reproj) <- colnames(orgdata) reproj <- new("dimRedData", data = reproj, meta = appl.meta) return(reproj) } res <- new( "dimRedResult", data = new("dimRedData", data = data, meta = meta), org.data = orgdata, apply = appl, inverse = inv, has.org.data = keep.org.data, has.apply = TRUE, has.inverse = TRUE, method = "PCA_L1", pars = pars ) return(res) }) ) dimRed/R/dimRedResult-class.R0000644000176200001440000001544413371631672015531 0ustar liggesusers#' @include misc.R #' @include dimRedData-class.R NULL #' Class "dimRedResult" #' #' A class to hold the results of of a dimensionality reduction. #' #' @slot data Output data of class dimRedData. #' @slot org.data original data, a matrix. #' @slot apply a function to apply the method to out-of-sampledata, #' may not exist. #' @slot inverse a function to calculate the original coordinates from #' reduced space, may not exist. #' @slot has.org.data logical, if the original data is included in the object. #' @slot has.apply logical, if a forward method is exists. #' @slot has.inverse logical if an inverse method exists. #' @slot method saves the method used. #' @slot pars saves the parameters used. #' @slot other.data other data produced by the method, e.g. a distance matrix. #' #' @examples #' ## Create object by embedding data #' iris.pca <- embed(loadDataSet("Iris"), "PCA") #' #' ## Convert the result to a data.frame #' head(as(iris.pca, "data.frame")) #' head(as.data.frame(iris.pca)) #' #' ## There are no nameclashes to avoid here: #' head(as.data.frame(iris.pca, #' org.data.prefix = "", #' meta.prefix = "", #' data.prefix = "")) #' #' ## Print it more or less nicely: #' print(iris.pca) #' #' ## Get the embedded data as a dimRedData object: #' getDimRedData(iris.pca) #' #' ## Get the original data including meta information: #' getOrgData(iris.pca) #' #' @family dimRedResult #' @export dimRedResult #' @exportClass dimRedResult dimRedResult <- setClass( "dimRedResult", slots = c( data = "dimRedData", org.data = "matrix", apply = "function", inverse = "function", has.org.data = "logical", has.apply = "logical", has.inverse = "logical", method = "character", pars = "list", other.data = "list" ), prototype = list( data = new("dimRedData"), org.data = matrix(numeric(0), 0, 0), apply = function(x) NA, inverse = function(x) NA, has.org.data = FALSE, has.apply = FALSE, has.inverse = FALSE, method = "", pars = list(), other.data = list() ) ) setAs( from = "dimRedResult", to = "data.frame", def = function(from){ if (from@has.org.data) { org.data <- from@org.data names(org.data) <- paste("org", names(org.data), sep = ".") cbind(as(from@data, "data.frame"), as.data.frame(org.data)) } else { as(from@data, "data.frame") } } ) #' @importFrom stats predict #' @export setGeneric( "predict", function(object, ...) standardGeneric("predict"), useAsDefault = stats::predict ) #' @describeIn dimRedResult apply a trained method to new data, does not work #' with all methods, will give an error if there is no \code{apply}. #' In some cases the apply function may only be an approximation. #' @param xnew new data, of type \code{\link{dimRedData}} #' #' @export setMethod(f = "predict", signature = "dimRedResult", definition = function(object, xnew) { if (object@has.apply) object@apply(xnew) else stop("object does not have an apply function") }) #' @export setGeneric( "inverse", function(object, ...) standardGeneric("inverse") ) #' @describeIn dimRedResult inverse transformation of embedded data, does not #' work with all methods, will give an error if there is no \code{inverse}. #' In some cases the apply function may only be an approximation. #' @param ynew embedded data, of type \code{\link{dimRedData}} #' #' @aliases inverse #' @export setMethod(f = "inverse", signature = c("dimRedResult"), definition = function(object, ynew) { if (object@has.inverse) object@inverse(ynew) else stop("object does not have an inverse function") }) #' @param x Of class \code{dimRedResult} #' @param org.data.prefix Prefix for the columns of the org.data slot. #' @param meta.prefix Prefix for the columns of \code{x@@data@@meta}. #' @param data.prefix Prefix for the columns of \code{x@@data@@data}. #' #' @describeIn dimRedResult convert to \code{data.frame} #' @export setMethod(f = "as.data.frame", signature = c("dimRedResult"), definition = function(x, org.data.prefix = "org.", meta.prefix = "meta.", data.prefix = "") { tmp <- list() if (nrow(x@data@meta) > 0){ tmp$meta <- as.data.frame(x@data@meta) names(tmp$meta) <- paste0(meta.prefix, colnames(x@data@meta)) } tmp$data <- as.data.frame(x@data@data) names(tmp$data) <- paste0(data.prefix, colnames(x@data@data)) if (x@has.org.data){ tmp$org.data <- as.data.frame(x@org.data) names(tmp$org.data) <- paste0(org.data.prefix, colnames(x@org.data)) } names(tmp) <- NULL data.frame(tmp, stringsAsFactors = FALSE) }) #' @param object Of class \code{dimRedResult} #' @describeIn dimRedResult Get the parameters with which the method #' was called. #' @export setMethod( f = "getPars", signature = "dimRedResult", definition = function (object) { object@pars } ) #' @describeIn dimRedResult Get the number of embedding dimensions. #' @export setMethod( f = "getNDim", signature = "dimRedResult", definition = function (object) { result <- getPars(object)$ndim if(is.null(result)) dim(object@data@data)[2] else result } ) #' @describeIn dimRedResult Method for printing. #' @import utils #' @export setMethod( f = "print", signature = "dimRedResult", definition = function(x) { cat("Method:\n") cat(x@method, "\n") cat("Parameters:\n") utils::str(x@pars) } ) #' @describeIn dimRedResult Get the original data and meta.data #' @export setMethod( f = "getOrgData", signature = "dimRedResult", definition = function(object) { return(new("dimRedData", data = object@org.data, meta = object@data@meta)) } ) #' @describeIn dimRedResult Get the embedded data #' @export setMethod( f = "getDimRedData", signature = "dimRedResult", definition = function(object) { return(object@data) } ) #' @describeIn dimRedResult Extract the number of embedding dimensions. #' #' @examples #' ## Get the number of variables: #' ndims(iris.pca) #' #' @export setMethod( "ndims", "dimRedResult", function(object) ncol(object@data@data) ) #' @describeIn dimRedResult Get other data produced by the method #' @export setMethod( f = "getOtherData", signature = "dimRedResult", definition = function(object) object@other.data ) dimRed/R/dimRed.R0000644000176200001440000000232413371631672013220 0ustar liggesusers#' @title The dimRed package #' #' @description This package simplifies dimensionality reduction in R by #' providing a framework of S4 classes and methods. dimRed collects #' dimensionality reduction methods that are implemented in R and implements #' others. It gives them a common interface and provides plotting #' functions for visualization and functions for quality assessment. #' #' Funding provided by the Department for Biogeochemical Integration, #' Empirical Inference of the Earth System Group, at the Max Plack #' Institute for Biogeochemistry, Jena. #' #' @references #' #' Lee, J.A., Renard, E., Bernard, G., Dupont, P., Verleysen, M., #' 2013. Type 1 and 2 mixtures of Kullback-Leibler divergences as cost #' functions in dimensionality reduction based on similarity #' preservation. Neurocomputing. 112, #' 92-107. doi:10.1016/j.neucom.2012.12.036 #' #' Lee, J.A., Lee, J.A., Verleysen, M., 2008. Rank-based quality #' assessment of nonlinear dimensionality reduction. Proceedings of #' ESANN 2008 49-54. #' #' Chen, L., Buja, A., 2006. Local Multidimensional Scaling for #' Nonlinear Dimension Reduction, Graph Layout and Proximity Analysis. #' #' #' @import methods #' @importFrom magrittr %>% #' "_PACKAGE" dimRed/R/embed.R0000644000176200001440000001217513371631672013075 0ustar liggesusers#' dispatches the different methods for dimensionality reduction #' #' wraps around all dimensionality reduction functions. #' #' Method must be one of \code{\link{dimRedMethodList}()}, partial matching #' is performed. All parameters start with a dot, to avoid clashes #' with partial argument matching (see the R manual section 4.3.2), if #' there should ever occur any clashes in the arguments, call the #' function with all arguments named, e.g. \code{embed(.data = dat, #' .method = "mymethod", .d = "some parameter")}. #' #' @param .data object of class \code{\link{dimRedData}}, will be converted to #' be of class \code{\link{dimRedData}} if necessary; see examples for #' details. #' @param .method character vector naming one of the dimensionality reduction #' techniques. #' @param .mute a character vector containing the elements you want to mute #' (\code{c("message", "output")}), defaults to \code{character(0)}. #' @param .keep.org.data \code{TRUE}/\code{FALSE} keep the original data. #' @param ... the parameters, internally passed as a list to the dimensionality #' reduction method as \code{pars = list(...)} #' @return an object of class \code{\link{dimRedResult}} #' #' @examples #' ## embed a data.frame using a formula: #' as.data.frame( #' embed(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, #' iris, "PCA") #' ) #' #' ## embed a data.frame and return a data.frame #' as.data.frame(embed(iris[, 1:4], "PCA")) #' #' ## embed a matrix and return a data.frame #' as.data.frame(embed(as.matrix(iris[, 1:4]), "PCA")) #' #' \dontrun{ #' ## embed dimRedData objects #' embed_methods <- dimRedMethodList() #' quality_methods <- dimRedQualityList() #' dataset <- loadDataSet("Iris") #' #' quality_results <- matrix(NA, length(embed_methods), length(quality_methods), #' dimnames = list(embed_methods, quality_methods)) #' embedded_data <- list() #' #' for (e in embed_methods) { #' message("embedding: ", e) #' embedded_data[[e]] <- embed(dataset, e, .mute = c("message", "output")) #' for (q in quality_methods) { #' message(" quality: ", q) #' quality_results[e, q] <- tryCatch( #' quality(embedded_data[[e]], q), #' error = function(e) NA #' ) #' } #' } #' #' print(quality_results) #' } #' @export setGeneric("embed", function(.data, ...) standardGeneric("embed"), valueClass = "dimRedResult") #' @describeIn embed embed a data.frame using a formula. #' @param .formula a formula, see \code{\link{as.dimRedData}}. #' @export setMethod( "embed", "formula", function(.formula, .data, .method = dimRedMethodList(), .mute = character(0), .keep.org.data = TRUE, ...) { if (!is.data.frame(.data)) stop(".data must be a data.frame") .data <- as.dimRedData(.formula, .data) embed(.data, .method, .mute, .keep.org.data, ...) } ) #' @describeIn embed Embed anything as long as it can be coerced to #' \code{\link{dimRedData}}. #' @export setMethod( "embed", "ANY", function(.data, .method = dimRedMethodList(), .mute = character(0), .keep.org.data = TRUE, ...) { embed(as(.data, "dimRedData"), .method, .mute, .keep.org.data, ...) } ) #' @describeIn embed Embed a dimRedData object #' @export setMethod( "embed", "dimRedData", function(.data, .method = dimRedMethodList(), .mute = character(0), #c("message", "output"), .keep.org.data = TRUE, ...) { .method <- if (all(.method == dimRedMethodList())) "PCA" else match.arg(.method) methodObject <- getMethodObject(.method) args <- list( data = as(.data, "dimRedData"), keep.org.data = .keep.org.data ) args$pars <- matchPars(methodObject, list(...)) devnull <- if (Sys.info()["sysname"] != "Windows") "/dev/null" else "NUL" if ("message" %in% .mute){ devnull1 <- file(devnull, "wt") sink(devnull1, type = "message") on.exit({ sink(file = NULL, type = "message") close(devnull1) }, add = TRUE) } if ("output" %in% .mute) { devnull2 <- file(devnull, "wt") sink(devnull2, type = "output") on.exit({ sink() close(devnull2) }, add = TRUE) } do.call(methodObject@fun, args) } ) getMethodObject <- function (method) { ## switch( ## method, ## graph_kk = kamada_kawai, ## graph_drl = drl, ## graph_fr = fruchterman_reingold, ## drr = drr, ## isomap = isomap, ## diffmap = diffmap, ## tsne = tsne, ## nmds = nmds, ## mds = mds, ## ica = fastica, ## pca = pca, ## lle = lle, ## loe = loe, ## soe = soe, ## leim = leim, ## kpca = kpca ## ) method <- match.arg(method, dimRedMethodList()) do.call(method, list()) } dimRed/R/rotate.R0000644000176200001440000001642513371631672013321 0ustar liggesusers ## rotate X in such a way that the values of Y have maximum squared ## correlation with the dimensions specified in axes. We optimize ## axes[1] first, then axes[2] without axes[1], ... ## we maximize the squared correlations of the original variables ## with the axis of the embeding and the final result is the sum_{axes} sum(squared(correlation(variables, axis))) setGeneric( "maximize_correlation", function(object, ...) standardGeneric("maximize_correlation"), valueClass = "dimRedResult" ) #' Maximize Correlation with the Axes #' #' Rotates the data in such a way that the correlation with the first #' \code{naxes} axes is maximized. #' #' Methods that do not use eigenvector decomposition, like t-SNE often #' do not align the data with axes according to the correlation of #' variables with the data. \code{maximize_correlation} uses the #' \code{\link[optimx]{optimx}} package to rotate the data in such a #' way that the original variables have maximum correlation with the #' embedding axes. #' #' @param object A dimRedResult object #' @param naxes the number of axes to optimize for. #' @param cor_method which correlation method to use #' #' @aliases maximize_correlation #' @export setMethod( "maximize_correlation", "dimRedResult", function(object, naxes = ncol(object@data@data), cor_method = "pearson"){ ## if (missing(naxes)) naxes <- ncol(object@data@data) ## if (missing(cor_method)) cor_method <- "pearson" if (!object@has.org.data) stop("object requires original data") if (length(naxes) != 1 || naxes < 1 || naxes > ncol(object@data@data)) stop("naxes must specify the numbers of axes to optimize for, ", "i.e. a single integer between 1 and ncol(object@data@data)") ## try to partially match cor_method: cor_method <- cor_method[pmatch(cor_method, c("pearson", "kendall", "spearman"))] if (is.na(cor_method)) stop("cor_method must match one of ", "'pearson', 'kendall', or 'spearman', ", "at least partially.") mcres <- .maximize_correlation(object@data@data, object@org.data, 1:naxes, cor_method) res <- object res@data@data <- mcres$rotated return(res) } ) .maximize_correlation <- function(X, Y, axes = 1:ncol(X), cor_method = "pearson"){ if (nrow(X) != nrow(Y)) stop("'X' and 'Y' must have the same number of rows") if (max(axes) > ncol(X)){ axes <- axes[ axes <= ncol(X) ] warning("'max(axes)' must be <= 'ncol(X)', removing some axes") } chckpkg("optimx") xndim <- ncol(X) without_axes <- integer(0) res <- list() for (axis in axes){ without_axes <- c(without_axes, axis) nplanes <- xndim - length(without_axes) planes <- matrix(NA, 2, nplanes) planes[1, ] <- axis planes[2, ] <- (1:xndim)[-without_axes] if (ncol(planes) == 0) break o <- optimx::optimx( par = rep(0, nplanes), fn = obj, method = "L-BFGS-B", lower = 0, upper = 2 * pi, X = as.matrix(X), Y = as.matrix(Y), axis = axis, without_axes = without_axes, cor_method = cor_method ) ## The result looks like this: ## p1 value fevals gevals niter convcode kkt1 kkt2 xtimes ## L-BFGS-B 0 -0.1613494 1 1 NA 0 FALSE NA 0.016 if (o$convcode > 0) stop("rotation did not converge.") res_idx <- length(res) + 1 res[[res_idx]] <- list() res[[res_idx]]$axis <- axis res[[res_idx]]$without_axes <- without_axes res[[res_idx]]$angs <- unname( unlist(o[1, 1:nplanes]) ) res[[res_idx]]$planes <- planes res[[res_idx]]$X <- rotate(res[[res_idx]]$angs, planes, X) res[[res_idx]]$cor <- -o$value } ## calculate the correlation for axes nres <- length(res) if (nres > 0) { ## the result is the sum of the mean squared correlations of the ## original variables with the axes. "res[[i]]$cor" contains the ## mean squared correlation of the variables with axis "i" res$result <- 0 for (i in 1:nres) res$result <- res$result + res[[i]]$cor ^ 2 ## res$result <- res$result / length(res) ## rotate the input to maximize correlations res$rotated <- X for (i in 1:nres) res$rotated <- rotate(res[[i]]$angs, res[[i]]$planes, res$rotated) } else { ## if we only had one dimension, simply return the means squared ## correlation and don't rotate res$result <- sum(correlate(X, Y, cor_method) ^ 2) res$rotated <- X } res } #### helper functions for rotation ## we create a number or rotation matrices around the 2d planes ## spanned by the orthonormal matrices, multiply them for a general ## rotation which is then applied to the data X rotate <- function (angs, planes, X) { ndim <- ncol(X) nplanes <- ncol(planes) if (length(angs) != nplanes) stop("length(angs) not equal to chose(ndim, 2)") ## loop over the planes to construct general rotation matrix rotmat <- diag(ndim) for (p in 1:nplanes) { ## 2d rotation ## possible optimization: create large rotation matrix ## directly and insert values linearly without a for loop rotmat2d <- matrix( c(cos(angs[p]), -sin(angs[p]), sin(angs[p]), cos(angs[p])), 2, 2, byrow = TRUE ) p_rotmat <- diag(ndim) for (i in 1:2) for (j in 1:2) p_rotmat[ planes[i, p], planes[j, p] ] <- rotmat2d[i, j] rotmat <- rotmat %*% p_rotmat } t(rotmat %*% t(X)) } get_planes <- function(ndims, axis, without_axes){ nplanes <- ndims - length(without_axes) planes <- matrix(NA, 2, nplanes) planes[1, ] <- axis planes[2, ] <- (1:ndims)[c(-axis, -without_axes)] planes } obj <- function(alpha, X, Y, axis, without_axes, cor_method = "pearson"){ ## correlation with first axis xndim <- ncol(X) planes <- get_planes(xndim, axis, without_axes) X2 <- rotate(alpha, planes, X) ## cor(x, y) returns a matrix with the correlations between the ## columns of x = X2 (rows) and the columns of y = Y (columns) we ## want the mean of squared correlations of all variables original ## variables with the first axis, i.e. we require the relevant ## (axis) column of the resulting matrix. ## Possible optimization: use only the relevant column of Y -mean(correlate( X2, Y, #use = "pairwise.complete.obs", method = cor_method )[axis, ] ^ 2) } correlate <- function (x, y, method, ...) { if (method != "kendall"){ return(stats::cor(x, y, method = method, ...)) } else { chckpkg("pcaPP") ## make the cor.fk method behave like cor for matrices: if (is.matrix(x) && is.matrix(y)) { res <- matrix( NA, nrow = ncol(x), ncol = ncol(y), dimnames = list(colnames(x), colnames(y)) ) for (i in 1:ncol(x)) { for (j in 1:ncol(y)){ res[i, j] <- pcaPP::cor.fk(x[, i], y[, j]) } } return(res) } else if (is.null(dim(x)) && is.null(dim(y))){ return(pcaPP::cor.fk(x, y)) } else { stop("something is wrong with the input of 'correlate()'") } } } dimRed/R/soe.R0000644000176200001440000000264213024273620012573 0ustar liggesusers## #' Soft Ordinal Embedding ## #' ## #' Instance of \code{\link{dimRedMethod}} for Soft Ordinal Embedding. ## #' ## #' For details see \code{\link[loe]{SOE}}. ## #' ## #' ## #' @examples ## #' dat <- loadDataSet("3D S Curve", n = 50) ## #' soe <- SOE() ## #' emb <- soe@fun(dat, soe@stdpars) ## #' ## #' ## #' plot(emb@data@data) ## #' ## #' ## #' @include dimRedResult-class.R ## #' @include dimRedMethod-class.R ## #' @export ## SOE <- setClass( ## "SOE", ## contains = "dimRedMethod", ## prototype = list( ## stdpars = list(d = stats::dist, knn = 50, ndim = 2), ## fun = function (data, ## pars, ## keep.org.data = TRUE) { ## chckpkg("loe") ## meta <- data@meta ## orgdata <- if (keep.org.data) data@data else NULL ## indata <- data@data ## outdata <- loe::SOE(loe::get.order(as.matrix(pars$d(indata))), ## N = nrow(indata), p = pars$ndim)$X ## colnames(outdata) <- paste0("SOE", 1:ncol(outdata)) ## return(new( ## "dimRedResult", ## data = new("dimRedData", ## data = outdata, ## meta = meta), ## org.data = orgdata, ## has.org.data = keep.org.data, ## method = "soe", ## pars = pars ## )) ## }) ## ) dimRed/R/misc.R0000644000176200001440000002202613371631672012750 0ustar liggesusers## if (!isClassUnion("missingORnumeric")) setClassUnion("missingORnumeric", c("numeric", "missing")) ## if (!isClassUnion("missingORcharacter")) setClassUnion("missingORcharacter", c("character", "missing")) ## if (!isClassUnion("missingORlogical")) setClassUnion("missingORlogical", c("logical", "missing")) ## if (!isClassUnion("missingORfunction")) setClassUnion("missingORfunction", c("function", "missing")) # Squared euclidean distance between points in A and B # taken from http://blog.felixriedel.com/2013/05/pairwise-distances-in-r/ pdist2 <- function (A, B) { an <- rowSums(A ^ 2) # apply(A, 1, function(rvec) crossprod(rvec, rvec)) bn <- rowSums(B ^ 2) # apply(B, 1, function(rvec) crossprod(rvec, rvec)) m <- nrow(A) n <- nrow(B) matrix(rep(an, n), nrow = m) + matrix(rep(bn, m), nrow = m, byrow = TRUE) - 2 * tcrossprod(A, B) } ## a + b ~ c + d ## becomes ## ~ c + d + 0 rhs <- function (formula) { fs <- as.character(formula)[3] stats::as.formula(paste("~", fs, "+ 0")) } ## a + b ~ c + d ## becomes ## ~ a + b + 0 lhs <- function (formula) { fs <- as.character(formula)[2] stats::as.formula(paste("~", fs, "+ 0")) } ## check if a package is installed chckpkg <- function (pkg) { if (!requireNamespace(pkg, quietly = TRUE)) { stop(paste0("require '", pkg, "' package, install it using install.packages('", pkg, "')")) } } ## create generics that appear in several different places #' Converts to data.frame #' #' General conversions of objects created by \code{dimRed} to \code{data.frame}. #' See class documentations for details (\code{\link{dimRedData}}, #' \code{\link{dimRedResult}}). For the documentation of this function in base #' package, see here: \code{\link[base]{as.data.frame.default}}. #' #' @param x The object to be converted #' @param row.names unused in \code{dimRed} #' @param optional unused in \code{dimRed} #' @param ... other arguments. setGeneric( "as.data.frame", function(x, row.names, optional, ...) standardGeneric("as.data.frame"), useAsDefault = base::as.data.frame, valueClass = "data.frame" ) #' Converts to dimRedData #' #' Conversion functions to dimRedData. #' #' @param formula The formula, left hand side is assigned to the meta slot right #' hand side is assigned to the data slot. #' @param ... other arguments. setGeneric( "as.dimRedData", function(formula, ...) standardGeneric("as.dimRedData"), valueClass = "dimRedData" ) #' Method getData #' #' Extracts the data slot. #' #' @param object The object to be converted. setGeneric("getData", function(object) standardGeneric("getData")) #' Method getMeta #' #' Extracts the meta slot. #' #' @param object The object to be converted. #' @param ... other arguments. setGeneric("getMeta", function(object, ...) standardGeneric("getMeta")) #' Method getPars #' #' Extracts the pars slot. #' #' @param object The object to be converted. #' @param ... other arguments. setGeneric("getPars", function (object, ...) standardGeneric("getPars")) #' Method getNDim #' #' Extract the number of embedding dimensions. #' #' @param object The object to get the dimensions from. #' @param ... other arguments. setGeneric("getNDim", function (object, ...) standardGeneric("getNDim")) #' Method getOrgData #' #' Extract the Original data. #' #' @param object The object to extract data from. #' @param ... other arguments. setGeneric("getOrgData", function (object, ...) standardGeneric("getOrgData")) #' Method getDimRedData #' #' Extract dimRedData. #' @param object The object to extract data from. #' @param ... other arguments. setGeneric("getDimRedData", function (object, ...) standardGeneric("getDimRedData")) #' Method getOtherData #' #' Extract other data produced by a dimRedMethod #' #' @param object The object to extract data from. #' @param ... other arguments. setGeneric("getOtherData", function (object, ...) standardGeneric("getOtherData"), valueClass = "list") #' Method print #' #' Imports the print method into the package namespace. #' #' @param x The object to be printed. #' @param ... Other arguments for printing. setGeneric("print", function(x, ...) standardGeneric("print")) #' Method ndims #' #' Extract the number of dimensions. #' #' @param object To extract the number of dimensions from. #' @param ... Arguments for further methods setGeneric("ndims", function (object, ...) standardGeneric("ndims"), valueClass = "integer") #' getSuggests #' #' Install packages wich are suggested by dimRed. #' #' By default dimRed will not install all the dependencies, because #' there are quite a lot and in case some of them are not available #' for your platform you will not be able to install dimRed without #' problems. #' #' To solve this I provide a function which automatically installes #' all the suggested packages. #' #' @examples #' \dontrun{ #' installSuggests() #' } #' @export installSuggests <- function () { "%w/o%" <- function(x, y) x[!x %in% y] pkgString <- installed.packages()["dimRed", "Suggests"] deps <- strsplit(pkgString, ", |,\n")[[1]] deps <- gsub("\n", "", deps) # Windows needs this installedPkgs <- rownames(installed.packages()) missingPkgs <- deps %w/o% installedPkgs if (length(missingPkgs) > 0) { message("The following packages are missing: ") cat(missingPkgs, "\n") message("installing ...") install.packages(missingPkgs) pkgString <- installed.packages()["dimRed", "Suggests"] installedPkgs <- rownames(installed.packages()) missingPkgs <- deps %w/o% installedPkgs if (length(missingPkgs) > 0) { message("Could not install the following packages:") cat(missingPkgs, "\n") message("please install manually or some methods will not work.") } else { message("All necessary packages installed") message("If things still don't work try 'update.packages()'") message("If it still does not work file a bugreport!!") } } else { message("All necessary packages installed") message("If things still don't work try 'update.packages()'") message("If it still does not work file a bugreport!!") } } ## input data(matrix or data frame) return knn graph implements ## "smart" choices on RANN::nn2 parameters we ignore radius search ## TODO: find out a good limit to switch from kd to bd trees COMMENT: ## bd trees are buggy, they dont work if there are duplicated data ## points and checking would neutralize the performance gain, so bd ## trees are not really usable. #' makeKNNgraph #' #' Create a K-nearest neighbor graph from data x. Uses #' \code{\link[RANN]{nn2}} as a fast way to find the neares neighbors. #' #' @param x data, a matrix, observations in rows, dimensions in #' columns #' @param k the number of nearest neighbors. #' @param eps number, if \code{eps > 0} the KNN search is approximate, #' see \code{\link[RANN]{nn2}} #' @param diag logical, if \code{TRUE} every edge of the returned #' graph will have an edge with weight \code{0} to itself. #' #' @return an object of type \code{\link[igraph]{igraph}} with edge #' weight being the distances. #' #' #' makeKNNgraph <- function(x, k, eps = 0, diag = FALSE){ ## requireNamespace("RANN") ## requireNamespace("igraph") ## consts INF_VAL <- 1.340781e+15 NA_IDX <- 0 BDKD_LIM <- 1000000 #todo: figure out a good value here ## select parameters M <- nrow(x) treetype <- "kd" # if (M < BDKD_LIM) "kd" else "bd" # see: # https://github.com/jefferis/RANN/issues/19 searchtype <- if (eps == 0) "standard" else "priority" ## RANN::nn2 returns the points in data with respect to query ## e.g. the rows in the output are the points in query and the ## columns the points in data. nn2res <- RANN::nn2(data = x, query = x, k = k + 1, treetype = treetype, searchtype = searchtype, eps = eps) ## create graph: the first ny nodes will be y, the last nx nodes ## will be x, if x != y g <- igraph::make_empty_graph(M, directed = FALSE) g[from = if (diag) rep(seq_len(M), times = k + 1) else rep(seq_len(M), times = k), to = if (diag) as.vector(nn2res$nn.idx) else as.vector(nn2res$nn.idx[, -1]), attr = "weight"] <- if (diag) as.vector(nn2res$nn.dists) else as.vector(nn2res$nn.dists[, -1]) return(g) } makeEpsSparseMatrix <- function(x, eps) { chckpkg("Matrix") n <- nrow(x) dd <- stats::dist(x) ddind <- dd < eps rows <- unlist(lapply(2:n, function(x) x:n), use.names = FALSE) cols <- rep(seq_len(n - 1), times = (n - 1):1) Matrix::sparseMatrix(i = rows[ddind], j = cols[ddind], x = dd[ddind], dims = c(n, n), symmetric = TRUE) } dimRed/R/nnmf.R0000644000176200001440000001227313562225201012743 0ustar liggesusers#' Non-Negative Matrix Factorization #' #' S4 Class implementing NNMF. #' #' NNMF is a method for decomposing a matrix into a smaller #' dimension such that the constraint that the data (and the #' projection) are not negative is taken into account. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' The method can take the following parameters: #' \describe{ #' \item{ndim}{The number of output dimensions.} #' \item{method}{character, which algorithm should be used. See #' \code{\link[NMF]{nmf}} for possible values. Defaults to #' "brunet"} #' \item{nrun}{integer, the number of times the computations are #' conducted. See \code{\link[NMF]{nmf}}} #' \item{seed}{integer, a value to control the random numbers used.} #' \item{options}{named list, other options to pass to \code{\link[NMF]{nmf}}} #' } #' #' @section Implementation: #' #' Wraps around \code{\link[NMF]{nmf}}. Note that the estimation uses random #' numbers. To create reproducible results, set the random number seed in the #' function call. Also, in many cases, the computations will be conducted #' in parallel using multiple cores. To disable this, use the option #' \code{.pbackend = NULL}. #' #' @references #' #' Lee, D.D., Seung, H.S., 1999. Learning the parts of objects by non-negative #' matrix factorization. Nature 401, 788-791. https://doi.org/10.1038/44565 #' #' @examples #' set.seed(4646) #' dat <- loadDataSet("Iris") #' emb <- embed(dat, "NNMF") #' #' plot(emb) #' #' # project new values: #' nn_proj <- predict(emb, dat[1:7]) #' plot(nn_proj) #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export NNMF #' @exportClass NNMF NNMF <- setClass( "NNMF", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2L, method = "brunet", nrun = 1, seed = sample.int(10^5, 1), options = list()), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("NMF") chckpkg("MASS") ## TODO: remove this, depends on https://github.com/renozao/NMF/issues/114 ## require("NMF") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL data <- data@data if (!is.matrix(data)) data <- as.matrix(data) # NMF expects variables in rows and samples in columns data <- t(data) if (pars$ndim > nrow(data)) stop("`ndim` should be less than the number of columns.", call. = FALSE) if (length(pars$method) != 1) stop("only supply one `method`", call. = FALSE) args <- list(x = quote(data), rank = pars$ndim, method = pars$method, nrun = pars$nrun, seed = pars$seed) if (length(pars$options) > 0) args <- c(args, pars$options) nmf_result <- do.call(NMF::nmf, args) # this should work but doesn't # call <- c(list(quote(NMF::nmf)), args) w <- NMF::basis(nmf_result) h <- t(NMF::coef(nmf_result)) colnames(w) <- paste0("NNMF", 1:ncol(w)) other.data <- list(w = w) colnames(h) <- paste0("NNMF", 1:ncol(h)) # evaluate results here for functions appl <- function (x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() dat <- if (inherits(x, "dimRedData")) x@data else x if (!is.matrix(dat)) dat <- as.matrix(dat) if (ncol(dat) != nrow(w)) stop("x must have the same number of columns ", "as the original data (", nrow(w), ")", call. = FALSE) res <- dat %*% t(MASS::ginv(w)) colnames(res) <- paste0("NNMF", 1:ncol(res)) scores <- new("dimRedData", data = res, meta = appl.meta) return(scores) } inv <- function (x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) > ncol(w)) stop("x must have less or equal number of dimensions ", "as the original data") res <- tcrossprod(proj, w) colnames(res) <- colnames(data) res <- new("dimRedData", data = res, meta = appl.meta) return(res) } ## inv <- function(x) { ## appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() ## proj <- if (inherits(x, "dimRedData")) x@data else x ## if (ncol(proj) > ncol(data)) ## stop("x must have less or equal number of dimensions ", ## "as the original data") ## reproj <- proj %*% other.data$H ## reproj <- new("dimRedData", data = reproj, meta = appl.meta) ## return(reproj) ## } res <- new( "dimRedResult", data = new("dimRedData", data = h, meta = meta), org.data = orgdata, apply = appl, inverse = inv, has.org.data = keep.org.data, has.apply = TRUE, has.inverse = TRUE, method = "NNMF", pars = pars, other.data = other.data ) return(res) }) ) dimRed/R/hlle.R0000644000176200001440000001025013562225201012722 0ustar liggesusers#' Hessian Locally Linear Embedding #' #' An S4 Class implementing Hessian Locally Linear Embedding (HLLE) #' #' HLLE uses local hessians to approximate the curvines and is an #' extension to non-convex subsets in lowdimensional space. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' HLLE can take the following parameters: #' \describe{ #' \item{knn}{neighborhood size} #' \item{ndim}{number of output dimensions} #' } #' #' @section Implementation: #' Own implementation, sticks to the algorithm in Donoho and Grimes #' (2003). Makes use of sparsity to speed up final embedding. #' #' @references #' Donoho, D.L., Grimes, C., 2003. Hessian eigenmaps: Locally linear #' embedding techniques for high-dimensional data. PNAS 100, #' 5591-5596. doi:10.1073/pnas.1031596100 #' #' @examples #' dat <- loadDataSet("3D S Curve", n = 300) #' emb <- embed(dat, "HLLE", knn = 15) #' plot(emb, type = "2vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export HLLE #' @exportClass HLLE HLLE <- setClass( "HLLE", contains = "dimRedMethod", prototype = list( stdpars = list(knn = 50, ndim = 2), fun = function(data, pars, keep.org.data = TRUE) { chckpkg("RSpectra") chckpkg("Matrix") chckpkg("RANN") if (pars$ndim < 2) stop("ndim must be 2 or larger.") if (is.null(pars$knn)) pars$knn <- 50 if (is.null(pars$ndim)) pars$ndim <- 2 indata <- data@data n <- nrow(indata) hs <- pars$ndim * (pars$ndim + 1) / 2 W <- Matrix::sparseMatrix(i = numeric(0), j = numeric(0), x = numeric(0), dims = c(n, hs * n)) ii <- jj <- ww <- list() ## Identify neighbors: message(Sys.time(), ": Finding nearest neighbors", sep = "") nnidx <- RANN::nn2(data = indata, query = indata, k = pars$knn + 1, treetype = "kd", "standard", eps = 0)$nn.idx#[, -1] message(Sys.time(), ": Calculating Hessian", sep = "") for (i in seq_len(n)) { cat(i, "/", n, "\r", sep = "") ## get neighborhood Nui <- indata[nnidx[i, ], , drop = FALSE] ## Form tangent coordinates: Nui <- sweep(Nui, 2, colMeans(Nui), "-") tc <- svd(Nui, nu = pars$ndim, nv = 0)$u ## Develop Hessian Estimator Xi <- cbind( 1, tc, tc ^ 2, apply(combn(seq_len(pars$ndim), 2), 2, function(x) tc[, x[1]] * tc[, x[2]]) ) tHi <- qr.Q(qr(Xi))[, -(1:(pars$ndim + 1)), drop = FALSE] ## Add quadratic form to hessian ii[[i]] <- rep(nnidx[i, ], hs) jj[[i]] <- rep((i - 1) * hs + (1:hs), each = ncol(nnidx)) ww[[i]] <- as.vector(tHi) } H <- as(Matrix::tcrossprod(Matrix::spMatrix( i = unlist(ii, FALSE, FALSE), j = unlist(jj, FALSE, FALSE), x = unlist(ww, FALSE, FALSE), nrow = n, ncol = n * hs) ), "dgCMatrix") ## Find null space: message(Sys.time(), ": Embedding", sep = "") ## eigs and eigs_sym converges much more reliably and faster ## with sigma = -eps than with which = "L*" outdata <- RSpectra::eigs_sym(H, k = pars$ndim + 1, sigma = -1e-5) message(paste(c("Eigenvalues:", format(outdata$values)), collapse = " ")) outdata <- outdata$vectors[, order(outdata$values)[-1], drop = FALSE] colnames(outdata) <- paste0("HLLE", seq_len(ncol(outdata))) message(Sys.time(), ": DONE", sep = "") return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = data@meta), org.data = if (keep.org.data) data@data else NULL, has.org.data = keep.org.data, method = "HLLE", pars = pars )) }) ) dimRed/R/plot.R0000644000176200001440000001665413371631672013005 0ustar liggesusers#' Plotting of dimRed* objects #' #' Plots a object of class dimRedResult and dimRedData. For the #' documentation of the plotting function in base see here: #' \code{\link{plot.default}}. #' #' Plotting functions for the classes usind in \code{dimRed}. they are #' intended to give a quick overview over the results, so they are #' somewhat inflexible, e.g. it is hard to modify color scales or #' plotting parameters. #' #' If you require more control over plotting, it is better to convert #' the object to a \code{data.frame} first and use the standard #' functions for plotting. #' #' @param x dimRedResult/dimRedData class, e.g. output of #' embedded/loadDataSet #' @param y Ignored #' @param type plot type, one of \code{c("pairs", "parpl", "2vars", #' "3vars", "3varsrgl")} #' @param col the columns of the meta slot to use for coloring, can be #' referenced as the column names or number of x@data #' @param vars the axes of the embedding to use for plotting #' @param ... handed over to the underlying plotting function. #' #' @examples #' scurve = loadDataSet("3D S Curve") #' plot(scurve, type = "pairs", main = "pairs plot of S curve") #' plot(scurve, type = "parpl") #' plot(scurve, type = "2vars", vars = c("y", "z")) #' plot(scurve, type = "3vars") #' #' @include mixColorSpaces.R #' @include dimRedData-class.R #' @importFrom graphics plot #' #' @aliases plot.dimRed #' @export setGeneric( "plot", function(x, y, ...) standardGeneric("plot"), useAsDefault = graphics::plot ) #' @describeIn plot Ploting of dimRedData objects #' @aliases plot.dimRedData #' @export setMethod( f = "plot", signature = c("dimRedData"), definition = function(x, type = "pairs", vars = seq_len(ncol(x@data)), col = seq_len(min(3, ncol(x@meta))), ...) { cols <- colorize(x@meta[, col, drop = FALSE]) switch( type, "pairs" = { chckpkg("graphics") graphics::pairs(x@data[, vars], col = cols, ... ) }, "parpl" = { chckpkg("MASS") MASS::parcoord(x@data[, vars], col = cols, ... ) }, "2vars" = { chckpkg("graphics") graphics::plot(x@data[, vars[1:2]], col = cols, ... ) }, "3vars" = { chckpkg("scatterplot3d") scatterplot3d::scatterplot3d(x@data[, vars[1:3]], color = cols, ...) }, "3varsrgl" = { chckpkg("rgl") rgl::plot3d(x@data[, vars[1:3]], col = cols, ... ) }, stop("wrong argument to plot.dimRedData") ) } ) #' @describeIn plot Ploting of dimRedResult objects. #' @aliases plot.dimRedResult #' @export setMethod( f = "plot", signature = c("dimRedResult"), definition = function (x, type = "pairs", vars = seq_len(ncol(x@data@data)), col = seq_len(min(3, ncol(x@data@meta))), ...) { plot(x = x@data, type = type, vars = vars, col = col, ...) } ) #' plot_R_NX #' #' Plot the R_NX curve for different embeddings. Takes a list of #' \code{\link{dimRedResult}} objects as input. #' Also the Area under the curve values are computed for a weighted K #' (see \link{AUC_lnK_R_NX} for details) and appear in the legend. #' #' @param x a list of \code{\link{dimRedResult}} objects. The names of the list #' will appear in the legend with the AUC_lnK value. #' @param ndim the number of dimensions, if \code{NA} the original number of #' embedding dimensions is used, can be a vector giving the embedding #' dimensionality for each single list element of \code{x}. #' @param weight the weight function used for K when calculating the AUC, one of #' \code{c("inv", "log", "log10")} #' @family Quality scores for dimensionality reduction #' @return A ggplot object, the design can be changed by appending #' \code{theme(...)} #' #' @examples #' #' ## define which methods to apply #' embed_methods <- c("Isomap", "PCA") #' ## load test data set #' data_set <- loadDataSet("3D S Curve", n = 200) #' ## apply dimensionality reduction #' data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) #' names(data_emb) <- embed_methods #' ## plot the R_NX curves: #' plot_R_NX(data_emb) + #' ggplot2::theme(legend.title = ggplot2::element_blank(), #' legend.position = c(0.5, 0.1), #' legend.justification = c(0.5, 0.1)) #' #' @export plot_R_NX <- function(x, ndim = NA, weight = "inv") { chckpkg("ggplot2") chckpkg("tidyr") chckpkg("scales") lapply( x, function(x) if (!inherits(x, "dimRedResult")) stop("x must be a list and ", "all items must inherit from 'dimRedResult'") ) rnx <- mapply(function(x, ndim) if(is.na(ndim)) R_NX(x) else R_NX(x, ndim), x = x, ndim = ndim) weight <- match.arg(weight, c("inv", "ln", "log", "log10")) w_fun <- switch( weight, inv = auc_ln_k_inv, log = auc_log_k, ln = auc_log_k, log10 = auc_log10_k, stop("wrong parameter for weight") ) auc <- apply(rnx, 2, w_fun) df <- as.data.frame(rnx) df$K <- seq_len(nrow(df)) qnxgrid <- expand.grid(K = df$K, rnx = seq(0.1, 0.9, by = 0.1)) ## TODO: FIND OUT WHY THIS AS IN THE PUBLICATION BUT IS WRONG! qnxgrid$qnx <- rnx2qnx(qnxgrid$rnx, K = qnxgrid$K, N = nrow(df)) # qnxgrid$rnx_group <- factor(qnxgrid$rnx) df <- tidyr::gather_(df, key_col = "embedding", value_col = "R_NX", names(x)) ggplot2::ggplot(df) + ggplot2::geom_line(ggplot2::aes_string(y = "R_NX", x = "K", color = "embedding")) + ## TODO: find out if this is wrong: ## ggplot2::geom_line(data = qnxgrid, ## mapping = ggplot2::aes_string(x = "K", y = "qnx", ## group = "rnx_group"), ## linetype = 2, ## size = 0.1) + ggplot2::geom_line(data = qnxgrid, mapping = ggplot2::aes_string(x = "K", y = "rnx", group = "rnx_group"), linetype = 3, size = 0.1) + ggplot2::scale_x_log10( labels = scales::trans_format("log10", scales::math_format()), expand = c(0, 0) ) + ggplot2::scale_y_continuous(expression(R[NX]), limits = c(0, 1), expand = c(0, 0)) + ggplot2::annotation_logticks(sides = "b") + ggplot2::scale_color_discrete( breaks = names(x), labels = paste(format(auc, digits = 3), names(x))) + ggplot2::labs(title = paste0( "R_NX vs. K", if (length(ndim) == 1 && !is.na(ndim)) paste0(", d = ", ndim) else "" )) + ggplot2::theme_classic() } dimRed/R/loe.R0000644000176200001440000000310713024273620012561 0ustar liggesusers ## this function produces segfaults and is super slow ## #' Local Ordinal Embedding ## #' ## #' Instance of \code{\link{dimRedMethod}} for Local Ordinal Embedding. ## #' ## #' For details see \code{\link[loe]{LOE}} ## #' ## #' @examples ## #' # for whatever reason the loe package has problems if I run this ## #' # with R CMD check, running it in the REPL works just fine ## #' dat <- loadDataSet("Iris")[sample(20)] ## #' loe <- LOE() ## #' emb <- loe@fun(dat, loe@stdpars) ## #' ## #' ## #' plot(emb@data@data) ## #' ## #' @include dimRedResult-class.R ## #' @include dimRedMethod-class.R ## #' @export ## LOE <- setClass( ## "LOE", ## contains = "dimRedMethod", ## prototype = list( ## stdpars = list(d = stats::dist, knn = 50, ndim = 2), ## fun = function (data, pars, ## keep.org.data = TRUE) { ## chckpkg("loe") ## meta <- data@meta ## orgdata <- if (keep.org.data) data@data else NULL ## indata <- data@data ## data.adj <- loe:::make.kNNG(as.matrix(pars$d(indata)), k = pars$knn) ## outdata <- loe::LOE(data.adj, p = pars$ndim, method = "MM")$X ## colnames(outdata) <- paste0("LOE", 1:ncol(outdata)) ## return(new( ## "dimRedResult", ## data = new("dimRedData", ## data = outdata, ## meta = meta), ## org.data = orgdata, ## has.org.data = keep.org.data, ## method = "loe", ## pars = pars ## )) ## }) ## ) dimRed/R/dataSets.R0000644000176200001440000001432013033377101013550 0ustar liggesusers#' Example Data Sets for dimensionality reduction #' #' A compilation of standard data sets that are often being used to #' showcase dimensionality reduction techniques. #' #' The argument \code{name} should be one of #' \code{dataSetList()}. Partial matching is possible, see #' \code{\link{match.arg}}. Generated data sets contain the internal #' coordinates of the manifold in the \code{meta} slot. Call #' \code{dataSetList()} to see what data sets are available. #' #' #' #' @param name A character vector that specifies the name of the data #' set. #' @param n In generated data sets the number of points to be #' generated, else ignored. #' @param sigma In generated data sets the standard deviation of the #' noise added, else ignored. #' @return \code{loadDataSet} an object of class #' \code{\link{dimRedData}}. \code{dataSetList()} return a #' character string with the implemented data sets #' #' @examples #' ## a list of available data sets: #' dataSetList() #' #' ## Load a data set: #' swissRoll <- loadDataSet("Swiss Roll") #' \donttest{plot(swissRoll, type = "3vars")} #' #' ## Load Iris data set, partial matching: #' loadDataSet("I") #' #' @name dataSets NULL #' @include dimRedData-class.R #' @rdname dataSets #' @export loadDataSet <- function (name = dataSetList(), n = 2000, sigma = 0.05) { name <- match.arg(name) switch( name, "Swiss Roll" = swissRoll(n, sigma), "Broken Swiss Roll" = brokenSwissRoll(n, sigma), "Helix" = helix(n, sigma), "Twin Peaks" = twinPeaks(n, sigma), "Sphere" = sphere(n, sigma), "FishBowl" = fishbowl(n, sigma), "Ball" = ball(n, sigma), "3D S Curve" = sCurve(n, sigma), "variable Noise Helix" = noisyHelix(n, sigma), "Cube" = cube(n, sigma), "Iris" = irisdata() ) } #' @rdname dataSets #' @export dataSetList <- function () { return(c( "Swiss Roll", "Broken Swiss Roll", "Helix", "Twin Peaks", "Sphere", "Ball", "FishBowl", "3D S Curve", "variable Noise Helix", "Iris", "Cube" )) } irisdata <- function() { dd <- as.matrix(datasets::iris[, 1:4]) new("dimRedData", data = dd, meta = datasets::iris[, 5, drop = FALSE]) } swissRoll <- function (n = 2000, sigma = 0.05) { x <- stats::runif(n, 1.5 * pi, 4.5 * pi) y <- stats::runif(n, 0, 30) new("dimRedData", data = swissRollMapping(x, y) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(x = x, y = y)) } brokenSwissRoll <- function (n = 2000, sigma = 0.05) { x <- c( stats::runif(floor(n / 2), 1.5 * pi, 2.7 * pi), stats::runif(ceiling(n / 2), 3.3 * pi, 4.5 * pi) ) y <- stats::runif(n, 0, 30) new("dimRedData", data = swissRollMapping(x, y) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(x = x, y = y)) } swissRollMapping <- function (x, y) { cbind(x = x * cos(x), y = y, z = x * sin(x)) } helix <- function (n = 2000, sigma = 0.05) { t <- stats::runif(n, 0, 2 * pi) new("dimRedData", data = helixMapping(t) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(t = t)) } helixMapping <- function (x) { cbind(x = (2 + cos(8 * x)) * cos(x), y = (2 + cos(8 * x)) * sin(x), z = (sin(8 * x))) } twinPeaks <- function (n = 2000, sigma = 0.05) { x <- stats::runif(n, -1, 1) y <- stats::runif(n, -1, 1) new("dimRedData", data = twinPeaksMapping(x, y) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(x = x, y = y)) } twinPeaksMapping <- function (x, y) { cbind(x = x, y = y, z = sin(pi * x) * tanh(3 * y)) } sphere <- function (n = 2000, sigma = 0.05) { phi <- stats::runif(n, 0, 2 * pi) psi <- acos(stats::runif(n, -1, 1)) new("dimRedData", data = sphereMapping(phi, psi) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(phi = phi, psi = psi)) } fishbowl <- function (n = 2000, sigma = 0.05) { phi <- stats::runif(n, 0, 2 * pi) psi <- acos(stats::runif(n, -1, 0.8)) new("dimRedData", data = sphereMapping(phi, psi) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(psi = psi)) } sphereMapping <- function (phi, psi) { cbind(x = cos(phi) * sin(psi), y = sin(phi) * sin(psi), z = cos(psi)) } ball <- function (n = 2000, sigma = 0.05) { phi <- stats::runif(n, 0, 2 * pi) psi <- acos(stats::runif(n, -1, 1)) ## make it uniformly distributed inside the sphere r <- stats::runif(n) ^ (1 / 3) new("dimRedData", data = ballMapping(phi, psi, r) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(phi = phi, psi = psi, r = r)) } ballMapping <- function (phi, psi, r) { cbind(x = r * cos(phi) * sin(psi), y = r * sin(phi) * sin(psi), z = r * cos(psi)) } sCurve <- function (n = 2000, sigma = 0.05) { t <- stats::runif(n, -1.5 * pi, 1.5 * pi) y <- stats::runif(n, 0, 2) new("dimRedData", data = sCurveMapping(t, y) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(x = t, y = y)) } sCurveMapping <- function (t, y) { cbind(x = sin(t), y = y, z = sign(t) * (cos(t) - 1)) } noisyHelix <- function (n = 2000, sigma = 0.05) { t <- stats::runif(n, 0, 4 * pi) min_noise <- 0.1 max_noise <- 1.4 new("dimRedData", data = noisyHelixMapping(t, min_noise, max_noise) + stats::rnorm(3 * n, sd = sigma), meta = data.frame(t = t)) } noisyHelixMapping <- function(t, min_noise, max_noise) { make_noise <- function (t){ stats::rnorm(length(t), sd = t * max_noise / max(t) + min_noise) } cbind(x = 3 * cos(t) + make_noise(t), y = 3 * sin(t) + make_noise(t), z = 2 * t + make_noise(t)) } cube <- function(n = 2000, sigma = 0.05){ tmp <- cbind(x = stats::runif(n) + stats::rnorm(n, sd = sigma), y = stats::runif(n) + stats::rnorm(n, sd = sigma), z = stats::runif(n) + stats::rnorm(n, sd = sigma)) new("dimRedData", data = tmp, meta = tmp) } dimRed/R/drr.R0000644000176200001440000001444413562225201012576 0ustar liggesusers#' Dimensionality Reduction via Regression #' #' An S4 Class implementing Dimensionality Reduction via Regression (DRR). #' #' DRR is a non-linear extension of PCA that uses Kernel Ridge regression. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' DRR can take the following parameters: #' \describe{ #' \item{ndim}{The number of dimensions} #' \item{lambda}{The regularization parameter for the ridge #' regression.} #' \item{kernel}{The kernel to use for KRR, defaults to #' \code{"rbfdot"}.} #' \item{kernel.pars}{A list with kernel parameters, elements depend #' on the kernel used, \code{"rbfdot"} uses \code{"sigma"}.} #' \item{pca}{logical, should an initial pca step be performed, #' defaults to \code{TRUE}.} #' \item{pca.center}{logical, should the data be centered before the #' pca step. Defaults to \code{TRUE}.} #' \item{pca.scale}{logical, should the data be scaled before the #' pca ste. Defaults to \code{FALSE}.} #' \item{fastcv}{logical, should \code{\link[CVST]{fastCV}} from the #' CVST package be used instead of normal cross-validation.} #' \item{fastcv.test}{If \code{fastcv = TRUE}, separate test data set for fastcv.} #' \item{cv.folds}{if \code{fastcv = FALSE}, specifies the number of #' folds for crossvalidation.} #' \item{fastkrr.nblocks}{integer, higher values sacrifice numerical #' accuracy for speed and less memory, see below for details.} #' \item{verbose}{logical, should the cross-validation results be #' printed out.} #' } #' #' @section Implementation: #' Wraps around \code{\link[DRR]{drr}}, see there for details. DRR is #' a non-linear extension of principal components analysis using Kernel #' Ridge Regression (KRR, details see \code{\link[CVST]{constructKRRLearner}} #' and \code{\link[DRR]{constructFastKRRLearner}}). Non-linear #' regression is used to explain more variance than PCA. DRR provides #' an out-of-sample extension and a backward projection. #' #' The most expensive computations are matrix inversions therefore the #' implementation profits a lot from a multithreaded BLAS library. #' The best parameters for each KRR are determined by cross-validaton #' over all parameter combinations of \code{lambda} and #' \code{kernel.pars}, using less parameter values will speed up #' computation time. Calculation of KRR can be accelerated by #' increasing \code{fastkrr.nblocks}, it should be smaller than #' n^{1/3} up to sacrificing some accuracy, for details see #' \code{\link[DRR]{constructFastKRRLearner}}. Another way to speed up #' is to use \code{pars$fastcv = TRUE} which might provide a more #' efficient way to search the parameter space but may also miss the #' global maximum, I have not ran tests on the accuracy of this method. #' #' #' #' @references #' Laparra, V., Malo, J., Camps-Valls, G., #' 2015. Dimensionality Reduction via Regression in Hyperspectral #' Imagery. IEEE Journal of Selected Topics in Signal Processing #' 9, 1026-1036. doi:10.1109/JSTSP.2015.2417833 #' #' @examples #' \dontrun{ #' dat <- loadDataSet("variable Noise Helix", n = 200)[sample(200)] #' #' emb <- embed(dat, "DRR", ndim = 3) #' #' plot(dat, type = "3vars") #' plot(emb, type = "3vars") #' #' # We even have function to reconstruct, also working for only the first few dimensions #' rec <- inverse(emb, getData(getDimRedData(emb))[, 1, drop = FALSE]) #' plot(rec, type = "3vars") #' } #' #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @import DRR #' @family dimensionality reduction methods #' @export DRR #' @exportClass DRR DRR <- setClass( "DRR", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, lambda = c(0, 10 ^ (-3:2)), kernel = "rbfdot", kernel.pars = list(sigma = 10 ^ (-3:4)), pca = TRUE, pca.center = TRUE, pca.scale = FALSE, fastcv = FALSE, cv.folds = 5, fastcv.test = NULL, fastkrr.nblocks = 4, verbose = TRUE), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("DRR") chckpkg("kernlab") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data res <- do.call(DRR::drr, c(list(X = indata), pars)) outdata <- res$fitted.data colnames(outdata) <- paste0("DRR", 1:ncol(outdata)) appl <- function(x){ appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != ncol(data@data)) stop("x must have the same number of dimensions ", "as the original data") appl.out <- new("dimRedData", data = res$apply(proj), meta = appl.meta) dimnames(appl.out@data) <- list( rownames(x), paste0("DRR", seq_len(ncol(appl.out@data))) ) return(appl.out) } inv <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) > ncol(data@data)) stop("x must have less or equal number of dimensions ", "as the original data") inv.out <- new("dimRedData", data = res$inverse(proj), meta = appl.meta) dimnames(inv.out@data) <- list(rownames(proj), colnames(data@data)) return(inv.out) } return( new("dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, apply = appl, inverse = inv, has.org.data = keep.org.data, has.apply = TRUE, has.inverse = TRUE, method = "drr", pars = pars ) ) }) ) dimRed/R/pca.R0000644000176200001440000001014113562225201012540 0ustar liggesusers#' Principal Component Analysis #' #' S4 Class implementing PCA. #' #' PCA transforms the data in orthogonal components so that the first #' axis accounts for the larges variance in the data, all the #' following axes account for the highest variance under the #' constraint that they are orthogonal to the preceding axes. PCA is #' sensitive to the scaling of the variables. PCA is by far the #' fastest and simples method of dimensionality reduction and should #' probably always be applied as a baseline if other methods are tested. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' PCA can take the following parameters: #' \describe{ #' \item{ndim}{The number of output dimensions.} #' \item{center}{logical, should the data be centered, defaults to \code{TRUE}.} #' \item{scale.}{logical, should the data be scaled, defaults to \code{FALSE}.} #' } #' #' @section Implementation: #' #' Wraps around \code{\link{prcomp}}. Because PCA can be reduced to a #' simple rotation, forward and backward projection functions are #' supplied. #' #' @references #' #' Pearson, K., 1901. On lines and planes of closest fit to systems of points in #' space. Philosophical Magazine 2, 559-572. #' #' @examples #' dat <- loadDataSet("Iris") #' emb <- embed(dat, "PCA") #' #' plot(emb, type = "2vars") #' plot(inverse(emb, getDimRedData(emb)), type = "3vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export PCA #' @exportClass PCA PCA <- setClass( "PCA", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, center = TRUE, scale. = FALSE), fun = function (data, pars, keep.org.data = TRUE) { ndim <- pars$ndim pars$ndim <- NULL meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL data <- data@data res <- do.call( prcomp, c(list(x = data), pars) ) # evaluate results here for functions data <- res$x[, seq_len(ndim), drop = FALSE] ce <- res$center sc <- res$scale rot <- res$rotation[, seq_len(ndim)] rerot <- t(rot) appl <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) != ncol(orgdata)) stop("x must have the same number of dimensions ", "as the original data") if (ce[1] != FALSE) proj <- t(apply(proj, 1, function(x) x - ce)) if (sc[1] != FALSE) proj <- t(apply(proj, 1, function(x) x / sc)) proj <- proj %*% rot proj <- new("dimRedData", data = proj, meta = appl.meta) return(proj) } inv <- function(x) { appl.meta <- if (inherits(x, "dimRedData")) x@meta else data.frame() proj <- if (inherits(x, "dimRedData")) x@data else x if (ncol(proj) > ncol(data)) stop("x must have less or equal number of dimensions ", "as the original data") d <- ncol(proj) reproj <- proj %*% rerot[seq_len(d), ] if (sc[1] != FALSE) reproj <- t(apply(reproj, 1, function(x) x * sc)) if (ce[1] != FALSE) reproj <- t(apply(reproj, 1, function(x) x + ce)) reproj <- new("dimRedData", data = reproj, meta = appl.meta) return(reproj) } res <- new( "dimRedResult", data = new("dimRedData", data = data, meta = meta), org.data = orgdata, apply = appl, inverse = inv, has.org.data = keep.org.data, has.apply = TRUE, has.inverse = TRUE, method = "PCA", pars = pars ) return(res) }) ) dimRed/R/graph_embed.R0000644000176200001440000002151013562225201014234 0ustar liggesusers#' Graph Embedding via the Kamada Kawai Algorithm #' #' An S4 Class implementing the Kamada Kawai Algorithm for graph embedding. #' #' Graph embedding algorithms se the data as a graph. Between the #' nodes of the graph exist attracting and repelling forces which can #' be modeled as electrical fields or springs connecting the #' nodes. The graph is then forced into a lower dimensional #' representation that tries to represent the forces betweent he nodes #' accurately by minimizing the total energy of the attracting and #' repelling forces. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' KamadaKawai can take the following parameters: #' \describe{ #' \item{ndim}{The number of dimensions, defaults to 2. Can only be 2 or 3} #' \item{knn}{Reduce the graph to keep only the neares neighbors. Defaults to 100.} #' \item{d}{The distance function to determine the weights of the graph edges. Defaults to euclidean distances.} #' } #' #' @section Implementation: #' Wraps around \code{\link[igraph]{layout_with_kk}}. The parameters #' maxiter, epsilon and kkconst are set to the default values and #' cannot be set, this may change in a future release. The DimRed #' Package adds an extra sparsity parameter by constructing a knn #' graph which also may improve visualization quality. #' #' @references #' #' Kamada, T., Kawai, S., 1989. An algorithm for drawing general undirected #' graphs. Information Processing Letters 31, 7-15. #' https://doi.org/10.1016/0020-0190(89)90102-6 #' #' @examples #' dat <- loadDataSet("Swiss Roll", n = 200) #' emb <- embed(dat, "KamadaKawai") #' plot(emb, type = "2vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export KamadaKawai #' @exportClass KamadaKawai KamadaKawai <- setClass( "KamadaKawai", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, knn = 100, d = stats::dist), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("igraph") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data outdata <- em_graph_layout( indata, graph_em_method = igraph::layout_with_kk, knn = pars$knn, d = pars$d, ndim = pars$ndim, weight.trans = I #pars$weight.trans ) colnames(outdata) <- paste0("KK", 1:ncol(outdata)) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "graph_kk", pars = pars )) }) ) #' Distributed Recursive Graph Layout #' #' An S4 Class implementing Distributed recursive Graph Layout. #' #' DrL uses a complex algorithm to avoid local minima in the graph #' embedding which uses several steps. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' DrL can take the following parameters: #' \describe{ #' \item{ndim}{The number of dimensions, defaults to 2. Can only be 2 or 3} #' \item{knn}{Reduce the graph to keep only the neares neighbors. Defaults to 100.} #' \item{d}{The distance function to determine the weights of the graph edges. Defaults to euclidean distances.} #' } #' #' @section Implementation: #' Wraps around \code{\link[igraph]{layout_with_drl}}. The parameters #' maxiter, epsilon and kkconst are set to the default values and #' cannot be set, this may change in a future release. The DimRed #' Package adds an extra sparsity parameter by constructing a knn #' graph which also may improve visualization quality. #' #' @references #' #' Martin, S., Brown, W.M., Wylie, B.N., 2007. Dr.l: Distributed Recursive #' (graph) Layout (No. dRl; 002182MLTPL00). Sandia National Laboratories. #' #' @examples #' \dontrun{ #' dat <- loadDataSet("Swiss Roll", n = 200) #' emb <- embed(dat, "DrL") #' plot(emb, type = "2vars") #' } #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export DrL #' @exportClass DrL DrL <- setClass( "DrL", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, knn = 100, d = stats::dist), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("igraph") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data outdata <- em_graph_layout( indata, graph_em_method = igraph::layout_with_drl, knn = pars$knn, d = pars$d, ndim = pars$ndim, weight.trans = I #pars$weight.trans ) colnames(outdata) <- paste0("DrL", 1:ncol(outdata)) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "graph_drl", pars = pars )) }) ) #' Fruchterman Reingold Graph Layout #' #' An S4 Class implementing the Fruchterman Reingold Graph Layout #' algorithm. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' \describe{ #' \item{ndim}{The number of dimensions, defaults to 2. Can only be 2 or 3} #' \item{knn}{Reduce the graph to keep only the neares neighbors. Defaults to 100.} #' \item{d}{The distance function to determine the weights of the graph edges. Defaults to euclidean distances.} #' } #' #' @section Implementation: #' Wraps around \code{\link[igraph]{layout_with_fr}}, see there for #' details. The Fruchterman Reingold algorithm puts the data into #' a circle and puts connected points close to each other. #' #' @references #' #' Fruchterman, T.M.J., Reingold, E.M., 1991. Graph drawing by force-directed #' placement. Softw: Pract. Exper. 21, 1129-1164. #' https://doi.org/10.1002/spe.4380211102 #' #' @examples #' dat <- loadDataSet("Swiss Roll", n = 100) #' emb <- embed(dat, "FruchtermanReingold") #' plot(emb, type = "2vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export FruchtermanReingold #' @exportClass FruchtermanReingold FruchtermanReingold <- setClass( "FruchtermanReingold", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, knn = 100, d = stats::dist), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("igraph") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data outdata <- em_graph_layout( indata, graph_em_method = igraph::layout_with_fr, knn = pars$knn, d = pars$d, ndim = pars$ndim, weight.trans = I #pars$weight.trans ) colnames(outdata) <- paste0("FR", 1:ncol(outdata)) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "graph_fr", pars = pars )) }) ) em_graph_layout <- function(data, graph_em_method, knn = 50, d = stats::dist, ndim = 2, weight.trans = I){ chckpkg("igraph") data.dist <- as.matrix(d(data)) data.graph <- construct_knn_graph(data.dist, knn) embed_graph(data.graph, graph_em_method, ndim = ndim) } embed_graph <- function(graph, f, weight.trans = I, ndim = 2){ f(graph, weights = weight.trans(igraph::E(graph)$weight), dim = ndim) } construct_knn_graph <- function (data.dist, knn) { chckpkg("igraph") chckpkg("coRanking") data.graph <- igraph::graph_from_adjacency_matrix( adjmatrix = data.dist, mode = "undirected", weighted = TRUE ) if (is.infinite(knn) || is.na(knn)) return(data.graph) ## else: remove all unnecessary edges data.rankm <- coRanking::rankmatrix(data.dist, input = "dist") data.rankm.ind <- data.rankm <= knn + 1 inds <- which( !(data.rankm.ind | t(data.rankm.ind)), arr.ind = TRUE ) data.graph[ from = inds[, 1], to = inds[, 2] ] <- FALSE return(data.graph) } dimRed/R/lle.R0000644000176200001440000000414013562225201012553 0ustar liggesusers#' Locally Linear Embedding #' #' An S4 Class implementing Locally Linear Embedding (LLE) #' #' LLE approximates the points in the manifold by linear combination #' of its neighbors. These linear combinations are the same inside the #' manifold and in highdimensional space. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' LLE can take the following parameters: #' \describe{ #' \item{knn}{the number of neighbors for the knn graph., defaults to 50.} #' \item{ndim}{the number of embedding dimensions, defaults to 2.} #' } #' #' @section Implementation: #' Wraps around \code{\link[lle]{lle}}, only #' exposes the parameters \code{k} and \code{m}. #' #' @references #' #' Roweis, S.T., Saul, L.K., 2000. Nonlinear Dimensionality Reduction #' by Locally Linear Embedding. Science 290, #' 2323-2326. doi:10.1126/science.290.5500.2323 #' #' @examples #' dat <- loadDataSet("3D S Curve", n = 500) #' emb <- embed(dat, "LLE", knn = 45) #' plot(emb, type = "2vars") #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @family dimensionality reduction methods #' @export LLE #' @exportClass LLE LLE <- setClass( "LLE", contains = "dimRedMethod", prototype = list( stdpars = list(knn = 50, ndim = 2), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("lle") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data outdata <- lle::lle(indata, k = pars$knn, m = pars$ndim)$Y if (is.null(dim(outdata))) { dim(outdata) <- c(length(outdata), 1) } colnames(outdata) <- paste0("LLE", 1:ncol(outdata)) return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "lle", pars = pars )) }) ) dimRed/R/dimRedData-class.R0000644000176200001440000001373013464507204015114 0ustar liggesusers#' @include misc.R NULL #' Class "dimRedData" #' #' A class to hold data for dimensionality reduction and methods. #' #' The class hast two slots, \code{data} and \code{meta}. The #' \code{data} slot contains a \code{numeric matrix} with variables in #' columns and observations in rows. The \code{meta} slot may contain #' a \code{data.frame} with additional information. Both slots need to #' have the same number of rows or the \code{meta} slot needs to #' contain an empty \code{data.frame}. #' #' See examples for easy conversion from and to \code{data.frame}. #' #' For plotting functions see \code{\link{plot.dimRedData}}. #' #' @slot data of class \code{matrix}, holds the data, observations in #' rows, variables in columns #' @slot meta of class \code{data.frame}, holds meta data such as #' classes, internal manifold coordinates, or simply additional #' data of the data set. Must have the same number of rows as the #' \code{data} slot or be an empty data frame. #' #' #' @examples #' ## Load an example data set: #' s3d <- loadDataSet("3D S Curve") #' #' ## Create using a constructor: #' #' ### without meta information: #' dimRedData(iris[, 1:4]) #' #' ### with meta information: #' dimRedData(iris[, 1:4], iris[, 5]) #' #' ### using slot names: #' dimRedData(data = iris[, 1:4], meta = iris[, 5]) #' #' ## Convert to a dimRedData objects: #' Iris <- as(iris[, 1:4], "dimRedData") #' #' ## Convert to data.frame: #' head(as(s3d, "data.frame")) #' head(as.data.frame(s3d)) #' head(as.data.frame(as(iris[, 1:4], "dimRedData"))) #' #' ## Extract slots: #' head(getData(s3d)) #' head(getMeta(s3d)) #' #' ## Get the number of observations: #' nrow(s3d) #' #' ## Subset: #' s3d[1:5, ] #' #' @family dimRedData #' @import methods #' @export dimRedData #' @exportClass dimRedData dimRedData <- setClass( "dimRedData", slots = c(data = "matrix", meta = "data.frame"), prototype = prototype(data = matrix(numeric(0), 0, 0), meta = data.frame()), validity = function (object) { retval <- NULL if (!is.matrix(object@data)) { retval <- c( retval, c("data must be a matrix with ", "observations in rows and dimensions in columns") ) } if (!is.numeric(object@data)) { retval <- c( retval, c("data must be numeric") ) } if ((nrow(object@meta) != 0) && (nrow(object@meta) != nrow(object@data))){ retval <- c( retval, c("data and meta must have the same numbers of rows") ) } return(if (is.null(retval)) TRUE else retval) } ) setMethod("initialize", signature = c("dimRedData"), function (.Object, data = matrix(numeric(0), 0, 0), meta = data.frame()) { data <- as.matrix(data) meta <- as.data.frame(meta) .Object <- callNextMethod() return(.Object) }) setAs(from = "ANY", to = "dimRedData", def = function(from) new("dimRedData", data = as.matrix(from))) setAs(from = "dimRedData", to = "data.frame", def = function(from) as.data.frame(from)) #' @param meta.prefix Prefix for the columns of the meta data names. #' @param data.prefix Prefix for the columns of the variable names. #' #' @family dimRedData #' @describeIn dimRedData convert to data.frame #' @export setMethod(f = "as.data.frame", signature = c("dimRedData"), definition = function(x, meta.prefix = "meta.", data.prefix = "") { tmp <- list() if (nrow(x@meta) > 0){ tmp$meta <- as.data.frame(x@meta, stringsAsFactors = FALSE) names(tmp$meta) <- paste0(meta.prefix, colnames(x@meta)) } tmp$data <- as.data.frame(x@data, stringsAsFactors = FALSE) names(tmp$data) <- paste0(data.prefix, colnames(x@data)) names(tmp) <- NULL data.frame(tmp, stringsAsFactors = FALSE) }) #' @param data Will be coerced into a \code{\link{data.frame}} with #' \code{\link{as.data.frame}} #' #' @examples #' ## create a dimRedData object using a formula #' as.dimRedData(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, #' iris)[1:5] #' #' @include misc.R #' @family dimRedData #' @describeIn as.dimRedData Convert a \code{data.frame} to a dimRedData #' object using a formula #' @export setMethod(f = "as.dimRedData", signature = c("formula"), definition = function(formula, data) { data <- as.data.frame(data) meta <- stats::model.frame(lhs(formula), data) data <- stats::model.matrix(rhs(formula), data) return(new("dimRedData", data = data, meta = meta)) }) #' @param object Of class dimRedData. #' @describeIn dimRedData Get the data slot. #' @export setMethod("getData", "dimRedData", function(object) object@data) #' @describeIn dimRedData Get the meta slot. #' @export setMethod("getMeta", "dimRedData", function(object) object@meta) #' @param x Of class dimRedData #' @describeIn dimRedData Get the number of observations. #' @export setMethod("nrow", "dimRedData", function(x) nrow(x@data)) #' @param i a valid index for subsetting rows. #' @examples #' ## Shuffle data: #' s3 <- s3d[nrow(s3d)] #' #' @describeIn dimRedData Subset rows. #' @export setMethod("[", signature(x = "dimRedData", i = "ANY"), function(x, i) { x@data <- x@data[i, , drop = FALSE] if (nrow(x@meta) != 0) x@meta <- x@meta[i, , drop = FALSE] # validObject returns a string with the description of what is wrong or # TRUE, so the following lines have to be as they are! vv <- validObject(x) if (vv == TRUE) return(x) else stop("cannot subset dimRedData object: \n", paste(vv, collapse = "\n")) }) #' @describeIn dimRedData Extract the number of Variables from the data. #' #' @examples #' ## Get the number of variables: #' ndims(s3d) #' #' @export setMethod("ndims", "dimRedData", function(object) ncol(object@data)) dimRed/R/quality.R0000644000176200001440000004706613753034327013516 0ustar liggesusers#' @include dimRedResult-class.R #' @include dimRedData-class.R #' @export setGeneric("quality", function (.data, ...) standardGeneric("quality"), valueClass = "numeric") #' Quality Criteria for dimensionality reduction. #' #' A collection of functions to compute quality measures on #' \code{\link{dimRedResult}} objects. #' #' @section Implemented methods: #' #' Method must be one of \code{"\link{Q_local}", "\link{Q_global}", #' "\link{mean_R_NX}", "\link{total_correlation}", #' "\link{cophenetic_correlation}", "\link{distance_correlation}", #' "\link{reconstruction_rmse}"} #' #' @section Rank based criteria: #' #' \code{Q_local}, \code{Q_global}, and \code{mean_R_NX} are #' quality criteria based on the Co-ranking matrix. \code{Q_local} #' and \code{Q_global} determine the local/global quality of the #' embedding, while \code{mean_R_NX} determines the quality of the #' overall embedding. They are parameter free and return a single #' number. The object must include the original data. The number #' returns is in the range [0, 1], higher values mean a better #' local/global embedding. #' #' @section Correlation based criteria: #' #' \code{total_correlation} calculates the sum of the mean squared #' correlations of the original axes with the axes in reduced #' dimensions, because some methods do not care about correlations #' with axes, there is an option to rotate data in reduced space to #' maximize this criterium. The number may be greater than one if more #' dimensions are summed up. #' #' \code{cophenetic_correlation} calculate the correlation between the #' lower triangles of distance matrices, the correlation and distance #' methods may be specified. The result is in range [-1, 1]. #' #' \code{distance_correlation} measures the independes of samples by #' calculating the correlation of distances. For details see #' \code{\link[energy]{dcor}}. #' #' @section Reconstruction error: #' #' \code{reconstruction_rmse} calculates the root mean squared error #' of the reconstrucion. \code{object} requires an inverse function. #' #' #' @references #' #' Lueks, W., Mokbel, B., Biehl, M., Hammer, B., 2011. How #' to Evaluate Dimensionality Reduction? - Improving the #' Co-ranking Matrix. arXiv:1110.3917 [cs]. #' #' Szekely, G.J., Rizzo, M.L., Bakirov, N.K., 2007. Measuring and #' testing dependence by correlation of distances. Ann. Statist. 35, #' 2769-2794. doi:10.1214/009053607000000505 #' #' Lee, J.A., Peluffo-Ordonez, D.H., Verleysen, M., 2015. Multi-scale #' similarities in stochastic neighbour embedding: Reducing #' dimensionality while preserving both local and global #' structure. Neurocomputing, 169, #' 246-261. doi:10.1016/j.neucom.2014.12.095 #' #' #' #' @param .data object of class \code{dimRedResult} #' @param .method character vector naming one of the methods #' @param .mute what output from the embedding method should be muted. #' @param ... the pameters, internally passed as a list to the #' quality method as \code{pars = list(...)} #' @return a number #' #' @examples #' \dontrun{ #' embed_methods <- dimRedMethodList() #' quality_methods <- dimRedQualityList() #' scurve <- loadDataSet("Iris") #' #' quality_results <- matrix(NA, length(embed_methods), length(quality_methods), #' dimnames = list(embed_methods, quality_methods)) #' embedded_data <- list() #' #' for (e in embed_methods) { #' message("embedding: ", e) #' embedded_data[[e]] <- embed(scurve, e, .mute = c("message", "output")) #' for (q in quality_methods) { #' message(" quality: ", q) #' quality_results[e, q] <- tryCatch( #' quality(embedded_data[[e]], q), #' error = function (e) NA #' ) #' } #' } #' #' print(quality_results) #' } #' @author Guido Kraemer #' @aliases quality quality.dimRedResult #' @family Quality scores for dimensionality reduction #' @describeIn quality Calculate a quality index from a dimRedResult object. #' @export setMethod( "quality", "dimRedResult", function (.data, .method = dimRedQualityList(), .mute = character(0), # c("output", "message"), ...) { method <- match.arg(.method) methodFunction <- getQualityFunction(method) args <- c(list(object = .data), list(...)) devnull <- if (Sys.info()["sysname"] != "Windows") "/dev/null" else "NUL" if ("message" %in% .mute){ devnull1 <- file(devnull, "wt") sink(devnull1, type = "message") on.exit({ sink(file = NULL, type = "message") close(devnull1) }, add = TRUE) } if ("output" %in% .mute) { devnull2 <- file(devnull, "wt") sink(devnull2, type = "output") on.exit({ sink() close(devnull2) }, add = TRUE) } do.call(methodFunction, args) } ) getQualityFunction <- function (method) { switch( method, Q_local = Q_local, Q_global = Q_global, mean_R_NX = mean_R_NX, AUC_lnK_R_NX = AUC_lnK_R_NX, total_correlation = total_correlation, cophenetic_correlation = cophenetic_correlation, distance_correlation = distance_correlation, reconstruction_rmse = reconstruction_rmse ) } #' @export setGeneric( "Q_local", function(object, ...) standardGeneric("Q_local"), valueClass = "numeric" ) #' Method Q_local #' #' Calculate the Q_local score to assess the quality of a dimensionality reduction. #' #' @param object of class dimRedResult. #' @param ndim use the first ndim columns of the embedded data for calculation. #' @family Quality scores for dimensionality reduction #' @aliases Q_local #' @export setMethod( "Q_local", "dimRedResult", function (object, ndim = getNDim(object)) { if (!object@has.org.data) stop("object requires original data") chckpkg("coRanking") Q <- coRanking::coranking(object@org.data, object@data@data[, seq_len(ndim), drop = FALSE]) nQ <- nrow(Q) N <- nQ + 1 Qnx <- diag(apply(apply(Q, 2, cumsum), 1, cumsum)) / seq_len(nQ) / N lcmc <- Qnx - seq_len(nQ) / nQ Kmax <- which.max(lcmc) Qlocal <- sum(Qnx[1:Kmax]) / Kmax return(as.vector(Qlocal)) } ) #' @export setGeneric( "Q_global", function(object, ...) standardGeneric("Q_global"), valueClass = "numeric" ) #' Method Q_global #' #' Calculate the Q_global score to assess the quality of a dimensionality reduction. #' #' @param object of class dimRedResult #' @family Quality scores for dimensionality reduction #' @aliases Q_global #' @export setMethod( "Q_global", "dimRedResult", function(object){ if (!object@has.org.data) stop("object requires original data") chckpkg("coRanking") Q <- coRanking::coranking(object@org.data, object@data@data) nQ <- nrow(Q) N <- nQ + 1 Qnx <- diag(apply(apply(Q, 2, cumsum), 1, cumsum)) / seq_len(nQ) / N lcmc <- Qnx - seq_len(nQ) / nQ Kmax <- which.max(lcmc) Qglobal <- sum(Qnx[(Kmax + 1):nQ]) / (N - Kmax) return(Qglobal) } ) #' @export setGeneric( "mean_R_NX", function(object, ...) standardGeneric("mean_R_NX"), valueClass = "numeric" ) #' Method mean_R_NX #' #' Calculate the mean_R_NX score to assess the quality of a dimensionality reduction. #' #' @param object of class dimRedResult #' @family Quality scores for dimensionality reduction #' @aliases mean_R_NX #' @export setMethod( "mean_R_NX", "dimRedResult", function(object) mean(R_NX(object)) ) #' @export setGeneric( "AUC_lnK_R_NX", function(object, ...) standardGeneric("AUC_lnK_R_NX"), valueClass = "numeric" ) #' Method AUC_lnK_R_NX #' #' Calculate the Area under the R_NX(ln K), used in Lee et. al. (2015). Note #' that despite the name, this does not weight the mean by the logarithm, but by #' 1/K. If explicit weighting by the logarithm is desired use \code{weight = #' "log"} or \code{weight = "log10"} #' #' The naming confusion originated from equation 17 in Lee et al (2015) and the #' name of this method may change in the future to avoid confusion. #' #' @references Lee, J.A., Peluffo-Ordonez, D.H., Verleysen, M., 2015. #' Multi-scale similarities in stochastic neighbour embedding: Reducing #' dimensionality while preserving both local and global structure. #' Neurocomputing 169, 246-261. https://doi.org/10.1016/j.neucom.2014.12.095 #' #' @param object of class dimRedResult #' @param weight the weight function used, one of \code{c("inv", "log", "log10")} #' @family Quality scores for dimensionality reduction #' @aliases AUC_lnK_R_NX #' @export setMethod( "AUC_lnK_R_NX", "dimRedResult", function(object, weight = "inv") { rnx <- R_NX(object) weight <- match.arg(weight, c("inv", "ln", "log", "log10")) switch( weight, inv = auc_ln_k_inv(rnx), log = auc_log_k(rnx), ln = auc_log_k(rnx), log10 = auc_log10_k(rnx), stop("wrong parameter for weight") ) } ) auc_ln_k_inv <- function(rnx) { Ks <- seq_along(rnx) return (sum(rnx / Ks) / sum(1 / Ks)) } auc_log_k <- function(rnx) { Ks <- seq_along(rnx) return (sum(rnx * log(Ks)) / sum(log(Ks))) } auc_log10_k <- function(rnx) { Ks <- seq_along(rnx) return (sum(rnx * log10(Ks)) / sum(log10(Ks))) } #' @export setGeneric( "total_correlation", function(object, ...) standardGeneric("total_correlation"), valueClass = "numeric" ) #' Method total_correlation #' #' Calculate the total correlation of the variables with the axes to #' assess the quality of a dimensionality reduction. #' #' @param object of class dimRedResult #' @param naxes the number of axes to use for optimization. #' @param cor_method the correlation method to use. #' @param is.rotated if FALSE the object is rotated. #' #' @family Quality scores for dimensionality reduction #' @aliases total_correlation #' @export setMethod( "total_correlation", "dimRedResult", function(object, naxes = ndims(object), cor_method = "pearson", is.rotated = FALSE){ if (!object@has.org.data) stop("object requires original data") if (length(naxes) != 1 || naxes < 1 || naxes > ncol(object@data@data)) stop("naxes must specify the numbers of axes to optimize for, ", "i.e. a single integer between 1 and ncol(object@data@data)") ## try to partially match cor_method: cor_methods <- c("pearson", "kendall", "spearman") cor_method <- cor_methods[pmatch(cor_method, cor_methods)] if (is.na(cor_method)) stop("cor_method must match one of ", "'pearson', 'kendall', or 'spearman', ", "at least partially.") if (!is.rotated) { rotated_result <- maximize_correlation( object, naxes, cor_method ) } else { rotated_result <- object } res <- 0 for (i in 1:naxes) res <- res + mean(correlate( rotated_result@data@data, rotated_result@org.data, cor_method )[i, ] ^ 2) return(res) } ) setGeneric("cophenetic_correlation", function(object, ...) standardGeneric("cophenetic_correlation"), valueClass = "numeric") #' Method cophenetic_correlation #' #' Calculate the correlation between the distance matrices in high and #' low dimensioal space. #' #' @param object of class dimRedResult #' @param d the distance function to use. #' @param cor_method The correlation method. #' @aliases cophenetic_correlation #' @family Quality scores for dimensionality reduction #' @export setMethod( "cophenetic_correlation", "dimRedResult", function(object, d = stats::dist, cor_method = "pearson"){ ## if (missing(d)) d <- stats::dist ## if (missing(cor_method)) cor_method <- "pearson" if (!object@has.org.data) stop("object requires original data") cor_methods <- c("pearson", "kendall", "spearman") cor_method <- cor_methods[pmatch(cor_method, cor_methods)] if (is.na(cor_method)) stop("cor_method must match one of ", "'pearson', 'kendall', or 'spearman', ", "at least partially.") d.org <- d(object@org.data) d.emb <- d(object@data@data) if (!inherits(d.org, "dist") || !inherits(d.emb, "dist")) stop("d must return a dist object") res <- correlate( d(object@org.data), d(object@data@data), cor_method ) return(res) } ) #' @export setGeneric( "distance_correlation", function(object) standardGeneric("distance_correlation"), valueClass = "numeric" ) #' Method distance_correlation #' #' Calculate the distance correlation between the distance matrices in #' high and low dimensioal space. #' #' @param object of class dimRedResult #' @aliases distance_correlation #' @family Quality scores for dimensionality reduction #' @export setMethod( "distance_correlation", "dimRedResult", function(object){ if (!object@has.org.data) stop("object requires original data") chckpkg("energy") energy::dcor(object@org.data, object@data@data) } ) #' @export setGeneric( "reconstruction_rmse", function(object) standardGeneric("reconstruction_rmse"), valueClass = "numeric" ) #' Method reconstruction_rmse #' #' Calculate the reconstruction root mean squared error a dimensionality reduction, the method must have an inverse mapping. #' #' @param object of class dimRedResult #' @aliases reconstruction_rmse #' @family Quality scores for dimensionality reduction #' @export setMethod( "reconstruction_rmse", "dimRedResult", function(object){ if (!object@has.org.data) stop("object requires original data") if (!object@has.inverse) stop("object requires an inverse function") recon <- object@inverse(object@data) rmse(recon@data, object@org.data) } ) #' @rdname quality #' #' @export dimRedQualityList <- function () { return(c("Q_local", "Q_global", "mean_R_NX", "AUC_lnK_R_NX", "total_correlation", "cophenetic_correlation", "distance_correlation", "reconstruction_rmse")) } #' @export setGeneric( "R_NX", function(object, ...) standardGeneric("R_NX"), valueClass = "numeric" ) #' Method R_NX #' #' Calculate the R_NX score from Lee et. al. (2013) which shows the neighborhood #' preservation for the Kth nearest neighbors, corrected for random point #' distributions and scaled to range [0, 1]. #' @param object of class dimRedResult #' @param ndim the number of dimensions to take from the embedded data. #' @family Quality scores for dimensionality reduction #' @aliases R_NX #' @export setMethod( "R_NX", "dimRedResult", function(object, ndim = getNDim(object)) { chckpkg("coRanking") if (!object@has.org.data) stop("object requires original data") Q <- coRanking::coranking(object@org.data, object@data@data[, seq_len(ndim), drop = FALSE]) nQ <- nrow(Q) N <- nQ + 1 Qnx <- diag(apply(apply(Q, 2, cumsum), 1, cumsum)) / seq_len(nQ) / N Rnx <- ((N - 1) * Qnx - seq_len(nQ)) / (N - 1 - seq_len(nQ)) Rnx[-nQ] } ) #' @export setGeneric( "Q_NX", function(object, ...) standardGeneric("Q_NX"), valueClass = "numeric" ) #' Method Q_NX #' #' Calculate the Q_NX score (Chen & Buja 2006, the notation in the #' publication is M_k). Which is the fraction of points that remain inside #' the same K-ary neighborhood in high and low dimensional space. #' #' @param object of class dimRedResult #' @family Quality scores for dimensionality reduction #' @aliases Q_NX #' @export setMethod( "Q_NX", "dimRedResult", function(object) { chckpkg("coRanking") Q <- coRanking::coranking(object@org.data, object@data@data) nQ <- nrow(Q) N <- nQ + 1 Qnx <- diag(apply(apply(Q, 2, cumsum), 1, cumsum)) / seq_len(nQ) / N Qnx } ) #'@export setGeneric( "LCMC", function(object, ...) standardGeneric("LCMC"), valueClass = "numeric" ) #' Method LCMC #' #' Calculates the Local Continuity Meta Criterion, which is #' \code{\link{Q_NX}} adjusted for random overlap inside the K-ary #' neighborhood. #' #' @param object of class dimRedResult #' @family Quality scores for dimensionality reduction #' @aliases LCMC #' @export setMethod( "LCMC", "dimRedResult", function(object) { chckpkg("coRanking") Q <- coRanking::coranking(object@org.data, object@data@data) nQ <- nrow(Q) N <- nQ + 1 lcmc <- diag(apply(apply(Q, 2, cumsum), 1, cumsum)) / seq_len(nQ) / N - seq_len(nQ) / nQ lcmc } ) rnx2qnx <- function(rnx, K = seq_along(rnx), N = length(rnx) + 1) { (rnx * (N - 1 - K) + K) / (N - 1) } qnx2rnx <- function(qnx, K = seq_along(qnx), N = length(qnx) + 1) { ((N - 1) * qnx - K) / (N - 1 - K) } #' @export setGeneric( "reconstruction_error", function(object, ...) standardGeneric("reconstruction_error"), valueClass = "numeric" ) #' Method reconstruction_error #' #' Calculate the error using only the first \code{n} dimensions of the embedded #' data. \code{error_fun} can either be one of \code{c("rmse", "mae")} to #' calculate the root mean square error or the mean absolute error respectively, #' or a function that takes to equally sized vectors as input and returns a #' single number as output. #' #' @param object of class dimRedResult #' @param n a positive integer or vector of integers \code{<= ndims(object)} #' @param error_fun a function or string indicating an error function, if #' indication a function it must take to matrices of the same size and return #' a scalar. #' @return a vector of number with the same length as \code{n} with the #' #' @examples #' \dontrun{ #' ir <- loadDataSet("Iris") #' ir.drr <- embed(ir, "DRR", ndim = ndims(ir)) #' ir.pca <- embed(ir, "PCA", ndim = ndims(ir)) #' #' rmse <- data.frame( #' rmse_drr = reconstruction_error(ir.drr), #' rmse_pca = reconstruction_error(ir.pca) #' ) #' #' matplot(rmse, type = "l") #' plot(ir) #' plot(ir.drr) #' plot(ir.pca) #' } #' @author Guido Kraemer #' @family Quality scores for dimensionality reduction #' @aliases reconstruction_error #' @export setMethod( "reconstruction_error", c("dimRedResult"), function (object, n = seq_len(ndims(object)), error_fun = "rmse") { if (any(n > ndims(object))) stop("n > ndims(object)") if (any(n < 1)) stop("n < 1") ef <- if (inherits(error_fun, "character")) { switch( error_fun, rmse = rmse, mae = mae ) } else if (inherits(error_fun, "function")) { error_fun } else { stop("error_fun must be a string or function, see documentation for details") } res <- numeric(length(n)) org <- getData(getOrgData(object)) for (i in seq_along(n)) { rec <- getData(inverse( object, getData(getDimRedData(object))[, seq_len(n[i]), drop = FALSE] )) res[i] <- ef(org, rec) } res } ) rmse <- function (x1, x2) sqrt(mean((x1 - x2) ^ 2)) mae <- function (x1, x2) mean(abs(x1 - x2)) dimRed/R/leim.R0000644000176200001440000001310014153203477012731 0ustar liggesusers#' Laplacian Eigenmaps #' #' An S4 Class implementing Laplacian Eigenmaps #' #' Laplacian Eigenmaps use a kernel and were originally developed to #' separate non-convex clusters under the name spectral clustering. #' #' @template dimRedMethodSlots #' #' @template dimRedMethodGeneralUsage #' #' @section Parameters: #' \code{LaplacianEigenmaps} can take the following parameters: #' \describe{ #' \item{ndim}{the number of output dimensions.} #' #' \item{sparse}{A character vector specifying hot to make the graph #' sparse, \code{"knn"} means that a K-nearest neighbor graph is #' constructed, \code{"eps"} an epsilon neighborhood graph is #' constructed, else a dense distance matrix is used.} #' #' \item{knn}{The number of nearest neighbors to use for the knn graph.} #' \item{eps}{The distance for the epsilon neighborhood graph.} #' #' \item{t}{Parameter for the transformation of the distance matrix #' by \eqn{w=exp(-d^2/t)}, larger values give less weight to #' differences in distance, \code{t == Inf} treats all distances != 0 equally.} #' \item{norm}{logical, should the normed laplacian be used?} #' } #' #' @section Implementation: #' Wraps around \code{\link[loe]{spec.emb}}. #' #' @references #' #' Belkin, M., Niyogi, P., 2003. Laplacian Eigenmaps for #' Dimensionality Reduction and Data Representation. Neural #' Computation 15, 1373. #' #' @examples #' dat <- loadDataSet("3D S Curve") #' emb <- embed(dat, "LaplacianEigenmaps") #' plot(emb@data@data) #' #' @include dimRedResult-class.R #' @include dimRedMethod-class.R #' @export LaplacianEigenmaps #' @exportClass LaplacianEigenmaps LaplacianEigenmaps <- setClass( "LaplacianEigenmaps", contains = "dimRedMethod", prototype = list( stdpars = list(ndim = 2, sparse = "knn", knn = 50, eps = 0.1, t = Inf, norm = TRUE), fun = function (data, pars, keep.org.data = TRUE) { chckpkg("loe") chckpkg("RSpectra") chckpkg("Matrix") meta <- data@meta orgdata <- if (keep.org.data) data@data else NULL indata <- data@data if (is.null(pars$d)) pars$d <- dist if (is.null(pars$knn)) pars$knn <- 50 if (is.null(pars$ndim)) pars$ndim <- 2 if (is.null(pars$t)) pars$t <- Inf if (is.null(pars$norm)) pars$norm <- TRUE message(Sys.time(), ": Creating weight matrix") W <- if (pars$sparse == "knn") { knng <- makeKNNgraph(indata, k = pars$knn, eps = 0, diag = TRUE) if (is.infinite(pars$t)){ knng <- igraph::set_edge_attr(knng, name = "weight", value = 1) } else { ea <- igraph::edge_attr(knng, name = "weight") knng <- igraph::set_edge_attr( knng, name = "weight", value = exp( -(ea ^ 2) / pars$t )) } igraph::as_adj(knng, sparse = TRUE, attr = "weight", type = "both") } else if (pars$sparse == "eps") { tmp <- makeEpsSparseMatrix(indata, pars$eps) tmp@x <- if (is.infinite(pars$t)) rep(1, length(tmp@i)) else exp(- (tmp@x ^ 2) / pars$t) ## diag(tmp) <- 1 as(tmp, "dgCMatrix") } else { # dense case tmp <- dist(indata) tmp[] <- if (is.infinite(pars$t)) 1 else exp( -(tmp ^ 2) / pars$t) tmp <- as.matrix(tmp) diag(tmp) <- 1 tmp } ## we don't need to test for symmetry, because we know the ## matrix is symmetric D <- Matrix::Diagonal(x = Matrix::rowSums(W)) L <- D - W ## for the generalized eigenvalue problem, we do not have a solver ## use A u = \lambda B u ## Lgen <- Matrix::Diagonal(x = 1 / Matrix::diag(D) ) %*% L ## but then we get negative eigenvalues and complex eigenvalues Lgen <- L message(Sys.time(), ": Eigenvalue decomposition") outdata <- if (pars$norm) { DS <- Matrix::Diagonal(x = 1 / sqrt(Matrix::diag(D))) RSpectra::eigs_sym(DS %*% Lgen %*% DS, k = pars$ndim + 1, sigma = -1e-5) } else { RSpectra::eigs_sym(Lgen, k = pars$ndim + 1, sigma = -1e-5) } message("Eigenvalues: ", paste(format(outdata$values), collapse = " ")) ## The eigenvalues are in decreasing order and we remove the ## smallest, which should be approx 0: outdata <- outdata$vectors[, order(outdata$values)[-1], drop = FALSE] if(ncol(outdata) > 0) { colnames(outdata) <- paste0("LEIM", seq_len(ncol(outdata))) } else { warning("no dimensions left, this is probably due to a badly conditioned eigenvalue decomposition.") } message(Sys.time(), ": DONE") return(new( "dimRedResult", data = new("dimRedData", data = outdata, meta = meta), org.data = orgdata, has.org.data = keep.org.data, method = "leim", pars = pars )) }) ) dimRed/NEWS.md0000644000176200001440000000143113464507204012560 0ustar liggesusers# dimRed 0.2.1 and 0.2.2 * Bugfix releases to pass CRAN tests # dimRed 0.2.0 * Added the R-Journal [paper](https://journal.r-project.org/archive/2018/RJ-2018-039/index.html "dimRed and coRanking") as Vignette * Added UMAP * Added NMF (thanks @topepo) * Added the possibility to return other data such as distance matrices/eigenvalues * Added Autoencoder * Added l1 PCA * Added `getNDim` * Added an `ndim` parameter to many quality functions. * fixed bug in kPCA if inverse was not computable. * added autoencoder # dimRed 0.1.0 * Fixed kPCA predict function and documentation typos (@topepo #2) * Added predict and inverse functions * Added a function to extract rotation matrices from PCA and FastICA # dimRed 0.0.3 * First version on CRAN dimRed/MD50000644000176200001440000001513714153365332012002 0ustar liggesusers8fb6bb466b44be0ffffde3351503ed68 *DESCRIPTION ae5a59342168733d9988af23c3ca4c2a *LICENSE 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liggesusersdimRed/inst/doc/dimensionality-reduction.R0000644000176200001440000001500414153217725020354 0ustar liggesusers## ----"pca_isomap_example",include=FALSE,fig.width=4,fig.height=4-------------- if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { library(dimRed); library(ggplot2); #library(dplyr); library(tidyr) ## define which methods to apply embed_methods <- c("Isomap", "PCA") ## load test data set data_set <- loadDataSet("3D S Curve", n = 1000) ## apply dimensionality reduction data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) names(data_emb) <- embed_methods ## plot data set, embeddings, and quality analysis ## plot(data_set, type = "3vars") ## lapply(data_emb, plot, type = "2vars") ## plot_R_NX(data_emb) add_label <- function(label) grid::grid.text(label, 0.2, 1, hjust = 0, vjust = 1, gp = grid::gpar(fontface = "bold", cex = 1.5)) ## pdf('~/phd/text/dimRedPackage/plots/plot_example.pdf', width = 4, height = 4) ## plot the results plot(data_set, type = "3vars", angle = 15, mar = c(3, 3, 0, 0), box = FALSE, grid = FALSE, pch = 16) add_label("a") par(mar = c(4, 4, 0, 0) + 0.1, bty = "n", las = 1) plot(data_emb$Isomap, type = "2vars", pch = 16) add_label("b") plot(data_emb$PCA, type = "2vars", pch = 16) add_label("d") ## calculate quality scores print( plot_R_NX(data_emb) + theme(legend.title = element_blank(), legend.position = c(0.5, 0.1), legend.justification = c(0.5, 0.1)) ) add_label("c") } else { # These cannot all be plot(1:10)!!! It's a mistery to me. plot(1:10) barplot(1:10) hist(1:10) plot(1:10) } ## ----eval=FALSE--------------------------------------------------------------- # ## define which methods to apply # embed_methods <- c("Isomap", "PCA") # ## load test data set # data_set <- loadDataSet("3D S Curve", n = 1000) # ## apply dimensionality reduction # data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) # names(data_emb) <- embed_methods # ## figure \ref{fig:plotexample}a, the data set # plot(data_set, type = "3vars") # ## figures \ref{fig:plotexample}b (Isomap) and \ref{fig:plotexample}d (PCA) # lapply(data_emb, plot, type = "2vars") # ## figure \ref{fig:plotexample}c, quality analysis # plot_R_NX(data_emb) ## ----include=FALSE------------------------------------------------------------ if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { library(dimRed) library(cccd) ## Load data ss <- loadDataSet("3D S Curve", n = 500) ## Parameter space kk <- floor(seq(5, 100, length.out = 40)) ## Embedding over parameter space emb <- lapply(kk, function(x) embed(ss, "Isomap", knn = x)) ## Quality over embeddings qual <- sapply(emb, function(x) quality(x, "Q_local")) ## Find best value for K ind_max <- which.max(qual) k_max <- kk[ind_max] add_label <- function(label){ par(xpd = TRUE) b = par("usr") text(b[1], b[4], label, adj = c(0, 1), cex = 1.5, font = 2) par(xpd = FALSE) } names(qual) <- kk } ## ----"select_k",include=FALSE,fig.width=11,fig.height=5----------------------- if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { par(mfrow = c(1, 2), mar = c(5, 4, 0, 0) + 0.1, oma = c(0, 0, 0, 0)) plot(kk, qual, type = "l", xlab = "k", ylab = expression(Q[local]), bty = "n") abline(v = k_max, col = "red") add_label("a") plot(ss, type = "3vars", angle = 15, mar = c(3, 3, 0, 0), box = FALSE, grid = FALSE, pch = 16) add_label("b") } else { plot(1:10) plot(1:10) } ## ----"knngraphs",include=FALSE,fig.width=8,fig.height=3----------------------- if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { par(mfrow = c(1, 3), mar = c(5, 4, 0, 0) + 0.1, oma = c(0, 0, 0, 0)) add_knn_graph <- function(ind) { nn1 <- nng(ss@data, k = kk[ind]) el <- get.edgelist(nn1) segments(x0 = emb[[ind]]@data@data[el[, 1], 1], y0 = emb[[ind]]@data@data[el[, 1], 2], x1 = emb[[ind]]@data@data[el[, 2], 1], y1 = emb[[ind]]@data@data[el[, 2], 2], col = "#00000010") } plot(emb[[2]]@data@data, type = "n", bty = "n") add_knn_graph(2) points(emb[[2]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("c") plot(emb[[ind_max]]@data@data, type = "n", bty = "n") add_knn_graph(ind_max) points(emb[[ind_max]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("d") plot(emb[[length(emb)]]@data@data, type = "n", bty = "n") add_knn_graph(length(emb)) points(emb[[length(emb)]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("e") } else { plot(1:10) plot(1:10) plot(1:10) } ## ----eval=FALSE--------------------------------------------------------------- # ## Load data # ss <- loadDataSet("3D S Curve", n = 500) # ## Parameter space # kk <- floor(seq(5, 100, length.out = 40)) # ## Embedding over parameter space # emb <- lapply(kk, function(x) embed(ss, "Isomap", knn = x)) # ## Quality over embeddings # qual <- sapply(emb, function(x) quality(x, "Q_local")) # ## Find best value for K # ind_max <- which.max(qual) # k_max <- kk[ind_max] ## ----"plot_quality",include=FALSE--------------------------------------------- if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { embed_methods <- dimRedMethodList() quality_methods <- c("Q_local", "Q_global", "AUC_lnK_R_NX", "cophenetic_correlation") iris_data <- loadDataSet("Iris") quality_results <- matrix( NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods) ) embedded_data <- list() for (e in embed_methods) { try(embedded_data[[e]] <- embed(iris_data, e)) for (q in quality_methods) try(quality_results[e,q] <- quality(embedded_data[[e]], q)) } quality_results <- quality_results[order(rowMeans(quality_results)), ] palette(c("#1b9e77", "#d95f02", "#7570b3", "#e7298a", "#66a61e")) col_hsv <- rgb2hsv(col2rgb(palette())) ## col_hsv["v", ] <- col_hsv["v", ] * 3 / 1 palette(hsv(col_hsv["h",], col_hsv["s",], col_hsv["v",])) par(mar = c(2, 8, 0, 0) + 0.1) barplot(t(quality_results), beside = TRUE, col = 1:4, legend.text = quality_methods, horiz = TRUE, las = 1, cex.names = 0.85, args.legend = list(x = "topleft", bg = "white", cex = 0.8)) } else { plot(1:10) } ## ----eval=FALSE--------------------------------------------------------------- # embed_methods <- dimRedMethodList() # quality_methods <- c("Q_local", "Q_global", "AUC_lnK_R_NX", # "cophenetic_correlation") # scurve <- loadDataSet("3D S Curve", n = 2000) # quality_results <- matrix( # NA, length(embed_methods), length(quality_methods), # dimnames = list(embed_methods, quality_methods) # ) # # embedded_data <- list() # for (e in embed_methods) { # embedded_data[[e]] <- embed(scurve, e) # for (q in quality_methods) # try(quality_results[e, q] <- quality(embedded_data[[e]], q)) # } dimRed/inst/doc/dimensionality-reduction.Rnw0000644000176200001440000017352413371631672020737 0ustar liggesusers\documentclass{article} %\VignetteEngine{knitr::knitr} %\VignetteIndexEntry{Dimensionality Reduction} %\VignetteKeyword{Dimensionality Reduction} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{hyperref} \usepackage{amsmath,amssymb} \usepackage{booktabs} \usepackage{tikz} \usetikzlibrary{trees} \usepackage[sectionbib,round]{natbib} \title{\pkg{dimRed} and \pkg{coRanking}---Unifying Dimensionality Reduction in R} \author{Guido Kraemer \and Markus Reichstein \and Miguel D.\ Mahecha} % these are taken from RJournal.sty: \makeatletter \DeclareRobustCommand\code{\bgroup\@noligs\@codex} \def\@codex#1{\texorpdfstring% {{\normalfont\ttfamily\hyphenchar\font=-1 #1}}% {#1}\egroup} \newcommand{\kbd}[1]{{\normalfont\texttt{#1}}} \newcommand{\key}[1]{{\normalfont\texttt{\uppercase{#1}}}} \DeclareRobustCommand\samp{`\bgroup\@noligs\@sampx} \def\@sampx#1{{\normalfont\texttt{#1}}\egroup'} \newcommand{\var}[1]{{\normalfont\textsl{#1}}} \let\env=\code \newcommand{\file}[1]{{`\normalfont\textsf{#1}'}} \let\command=\code \let\option=\samp \newcommand{\dfn}[1]{{\normalfont\textsl{#1}}} % \acronym is effectively disabled since not used consistently \newcommand{\acronym}[1]{#1} \newcommand{\strong}[1]{\texorpdfstring% {{\normalfont\fontseries{b}\selectfont #1}}% {#1}} \let\pkg=\strong \newcommand{\CRANpkg}[1]{\href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}}% \let\cpkg=\CRANpkg \newcommand{\ctv}[1]{\href{https://CRAN.R-project.org/view=#1}{\emph{#1}}} \newcommand{\BIOpkg}[1]{\href{https://www.bioconductor.org/packages/release/bioc/html/#1.html}{\pkg{#1}}} \makeatother \begin{document} \maketitle \abstract{ % This document is based on the manuscript of \citet{kraemer_dimred_2018} which was published in the R-Journal and has been modified and extended to fit the format of a package vignette and to match the extended functionality of the \pkg{dimRed} package. ``Dimensionality reduction'' (DR) is a widely used approach to find low dimensional and interpretable representations of data that are natively embedded in high-dimensional spaces. % DR can be realized by a plethora of methods with different properties, objectives, and, hence, (dis)advantages. The resulting low-dimensional data embeddings are often difficult to compare with objective criteria. % Here, we introduce the \CRANpkg{dimRed} and \CRANpkg{coRanking} packages for the R language. % These open source software packages enable users to easily access multiple classical and advanced DR methods using a common interface. % The packages also provide quality indicators for the embeddings and easy visualization of high dimensional data. % The \pkg{coRanking} package provides the functionality for assessing DR methods in the co-ranking matrix framework. % In tandem, these packages allow for uncovering complex structures high dimensional data. % Currently 15 DR methods are available in the package, some of which were not previously available to R users. % Here, we outline the \pkg{dimRed} and \pkg{coRanking} packages and make the implemented methods understandable to the interested reader. % } \section{Introduction} \label{sec:intro} Dimensionality Reduction (DR) essentially aims to find low dimensional representations of data while preserving their key properties. % Many methods exist in literature, optimizing different criteria: % maximizing the variance or the statistical independence of the projected data, % minimizing the reconstruction error under different constraints, % or optimizing for different error metrics, % just to name a few. % Choosing an inadequate method may imply that much of the underlying structure remains undiscovered. % Often the structures of interest in a data set can be well represented by fewer dimensions than exist in the original data. % Data compression of this kind has the additional benefit of making the encoded information better conceivable to our brains for further analysis tasks like classification or regression problems. % For example, the morphology of a plant's leaves, stems, and seeds reflect the environmental conditions the species usually grow in (e.g.,\ plants with large soft leaves will never grow in a desert but might have an advantage in a humid and shadowy environment). % Because the morphology of the entire plant depends on the environment, many morphological combinations will never occur in nature and the morphological space of all plant species is tightly constrained. % \citet{diaz_global_2016} found that out of six observed morphological characteristics only two embedding dimensions were enough to represent three quarters of the totally observed variability. % DR is a widely used approach for the detection of structure in multivariate data, and has applications in a variety of fields. % In climatology, DR is used to find the modes of some phenomenon, e.g.,\ the first Empirical Orthogonal Function of monthly mean sea surface temperature of a given region over the Pacific is often linked to the El Ni\~no Southern Oscillation or ENSO \citep[e.g.,\ ][]{hsieh_nonlinear_2004}. % In ecology the comparison of sites with different species abundances is a classical multivariate problem: each observed species adds an extra dimension, and because species are often bound to certain habitats, there is a lot of redundant information. Using DR is a popular technique to represent the sites in few dimensions, e.g.,\ \citet{aart_distribution_1972} matches wolfspider communities to habitat and \citet{morrall_soil_1974} match soil fungi data to soil types. (In ecology the general name for DR is ordination or indirect gradient analysis.) % Today, hyperspectral satellite imagery collects so many bands that it is very difficult to analyze and interpret the data directly. % Resuming the data into a set of few, yet independent, components is one way to reduce complexity \citep[e.g.,\ see][]{laparra_dimensionality_2015}. % DR can also be used to visualize the interiors of deep neural networks \citep[e.g.,\ see ][]{han_deep_2016}, where the high dimensionality comes from the large number of weights used in a neural network and convergence can be visualized by means of DR\@. % We could find many more example applications here but this is not the main focus of this publication. % The difficulty in applying DR is that each DR method is designed to maintain certain aspects of the original data and therefore may be appropriate for one task and inappropriate for another. % Most methods also have parameters to tune and follow different assumptions. The quality of the outcome may strongly depend on their tuning, which adds additional complexity. % DR methods can be modeled after physical models with attracting and repelling forces (Force Directed Methods), projections onto low dimensional planes (PCA, ICA), divergence of statistical distributions (SNE family), or the reconstruction of local spaces or points by their neighbors (LLE). % As an example for how changing internal parameters of a method can have a great impact, the breakthrough for Stochastic Neighborhood Embedding (SNE) methods came when a Student's $t$-distribution was used instead of a normal distribution to model probabilities in low dimensional space to avoid the ``crowding problem'', that is,\ a sphere in high dimensional space has a much larger volume than in low dimensional space and may contain too many points to be represented accurately in few dimensions. % The $t$-distribution, allows medium distances to be accurately represented in few dimensions by larger distances due to its heavier tails. % The result is called in $t$-SNE and is especially good at preserving local structures in very few dimensions, this feature made $t$-SNE useful for a wide array of data visualization tasks and the method became much more popular than standard SNE (around six times more citations of \citet{van_der_maaten_visualizing_2008} compared to \citet{hinton_stochastic_2003} in Scopus \citep{noauthor_scopus_nodate}). % There are a number of software packages for other languages providing collections of methods: In Python there is scikit-learn \citep{scikit-learn}, which contains a module for DR. In Julia we currently find ManifoldLearning.jl for nonlinear and MultivariateStats.jl for linear DR methods. % There are several toolboxes for DR implemented in Matlab \citep{van_der_maaten_dimensionality_2009, arenas-garcia_kernel_2013}. The Shogun toolbox \citep{soeren_sonnenburg_2017_1067840} implements a variety of methods for dimensionality reduction in C++ and offers bindings for a many common high level languages (including R, but the installation is anything but simple, as there is no CRAN package). % However, there is no comprehensive package for R and none of the former mentioned software packages provides means to consistently compare the quality of different methods for DR. % For many applications it can be difficult to objectively find the right method or parameterization for the DR task. % This paper presents the \pkg{dimRed} and \pkg{coRanking} packages for the popular programming language R. Together, they provide a standardized interface to various dimensionality reduction methods and quality metrics for embeddings. They are implemented using the S4 class system of R, making the packages both easy to use and to extend. The design goal for these packages is to enable researchers, who may not necessarily be experts in DR, to apply the methods in their own work and to objectively identify the most suitable methods for their data. % This paper provides an overview of the methods collected in the packages and contains examples as to how to use the packages. % The notation in this paper will be as follows: $X = [x_i]_{1\leq i \leq n}^T \in \mathbb{R}^{n\times p}$, and the observations $x_i \in \mathbb{R}^p$. % These observations may be transformed prior to the dimensionality reduction step (e.g.,\ centering and/or standardization) resulting in $X' = [x'_i]_{1\leq i \leq n}^T \in \mathbb{R}^{n\times p}$. % A DR method then embeds each vector in $X'$ onto a vector in $Y = [y_i]_{1\leq i \leq n}^T \in \mathbb{R}^{n\times q}$ with $y_i \in \mathbb{R}^q$, ideally with $q \ll p$. % Some methods provide an explicit mapping $f(x'_i) = y_i$. Some even offer an inverse mapping $f^{-1}(y_{i}) = \hat x'_{i}$, such that one can reconstruct a (usually approximate) sample from the low-dimensional representation. % For some methods, pairwise distances between points are needed, we set $d_{ij} = d(x_{i}, x_{j})$ and $\hat{d}_{ij} = d(y_i, y_j)$, where $d$ is some appropriate distance function. When referring to \code{functions} in the \pkg{dimRed} package or base R simply the function name is mentioned, functions from other packages are referenced with their namespace, as with \code{package::function}. \begin{figure}[htbp] \centering \input{classification_tree.tex} \caption{% Classification of dimensionality reduction methods. Methods in bold face are implemented in \pkg{dimRed}. Modified from \citet{van_der_maaten_dimensionality_2009}. }\label{fig:classification} \end{figure} \section{Dimensionality Reduction Methods} \label{sec:dimredtec} In the following section we do not aim for an exhaustive explanation to every method in \pkg{dimRed} but rather to provide a general idea on how the methods work. % An overview and classification of the most commonly used DR methods can be found in Figure~\ref{fig:classification}. In all methods, parameters have to be optimized or decisions have to be made, even if it is just about the preprocessing steps of data. % The \pkg{dimRed} package tries to make the optimization process for parameters as easy as possible, but, if possible, the parameter space should be narrowed down using prior knowledge. % Often decisions can be made based on theoretical knowledge. For example,\ sometimes an analysis requires data to be kept in their original scales and sometimes this is exactly what has to be avoided as when comparing different physical units. % Sometimes decisions based on the experience of others can be made, e.g.,\ the Gaussian kernel is probably the most universal kernel and therefore should be tested first if there is a choice. % All methods presented here have the embedding dimensionality, $q$, as a parameter (or \code{ndim} as a parameter for \code{embed}). % For methods based on eigenvector decomposition, the result generally does not depend on the number of dimensions, i.e.,\ the first dimension will be the same, no matter if we decide to calculate only two dimensions or more. % If more dimensions are added, more information is maintained, the first dimension is the most important and higher dimensions are successively less important. % This means, that a method based on eigenvalue decomposition only has to be run once if one wishes to compare the embedding in different dimensions. % In optimization based methods this is generally not the case, the number of dimensions has to be chosen a priori, an embedding of 2 and 3 dimensions may vary significantly, and there is no ordered importance of dimensions. % This means that comparing dimensions of optimization-based methods is computationally much more expensive. % We try to give the computational complexity of the methods. Because of the actual implementation, computation times may differ largely. % R is an interpreted language, so all parts of an algorithm that are implemented in R often will tend to be slow compared to methods that call efficient implementations in a compiled language. % Methods where most of the computing time is spent for eigenvalue decomposition do have very efficient implementations as R uses optimized linear algebra libraries. Although, eigenvalue decomposition itself does not scale very well in naive implementations ($\mathcal{O}(n^3)$). \subsection{PCA} \label{sec:pca} Principal Component Analysis (PCA) is the most basic technique for reducing dimensions. It dates back to \citet{pearson_lines_1901}. PCA finds a linear projection ($U$) of the high dimensional space into a low dimensional space $Y = XU$, maintaining maximum variance of the data. It is based on solving the following eigenvalue problem: \begin{equation} (C_{XX}-\lambda_k I)u_k=0\label{eq:pca} \end{equation} where $C_{XX} = \frac 1 n X^TX$ is the covariance matrix, $\lambda_k$ and $u_k$ are the $k$-th eigenvalue and eigenvector, and $I$ is the identity matrix. % The equation has several solutions for different values of $\lambda_k$ (leaving aside the trivial solution $u_k = 0$). % PCA can be efficiently applied to large data sets, because it computationally scales as $\mathcal{O}(np^2 + p^3)$, that is, it scales linearly with the number of samples and R uses specialized linear algebra libraries for such kind of computations. PCA is a rotation around the origin and there exist a forward and inverse mapping. % PCA may suffer from a scale problem, i.e.,\ when one variable dominates the variance simply because it is in a higher scale, to remedy this, the data can be scaled to zero mean and unit variance, depending on the use case, if this is necessary or desired. % Base R implements PCA in the functions \code{prcomp} and \code{princomp}; but several other implementations exist i.e., \BIOpkg{pcaMethods} from Bioconductor which implements versions of PCA that can deal with missing data. % The \pkg{dimRed} package wraps \code{prcomp}. \subsection{kPCA} \label{sec:kpca} Kernel Principal Component Analysis (kPCA) extends PCA to deal with nonlinear dependencies among variables. % The idea behind kPCA is to map the data into a high dimensional space using a possibly non-linear function $\phi$ and then to perform a PCA in this high dimensional space. % Some mathematical tricks are used for efficient computation. % If the columns of X are centered around $0$, then the principal components can also be computed from the inner product matrix $K = X^TX$. % Due to this way of calculating a PCA, we do not need to explicitly map all points into the high dimensional space and do the calculations there, it is enough to obtain the inner product matrix or kernel matrix $K \in \mathbb{R}^{n\times n}$ of the mapped points \citep{scholkopf_nonlinear_1998}. % Here is an example calculating the kernel matrix using a Gaussian kernel: \begin{equation}\label{eq:gauss} K = \phi(x_i)^T \phi(x_j) = \kappa(x_i, x_j) = \exp\left( -\frac{\| x_i- x_j\|^2}{2 \sigma^2} \right), \end{equation} where $\sigma$ is a length scale parameter accounting for the width of the kernel. % The other trick used is known as the ``representers theorem.'' The interested reader is referred to \citet{scholkopf_generalized_2001}. The kPCA method is very flexible and there exist many kernels for special purposes. The most common kernel function is the Gaussian kernel (Equation\ \ref{eq:gauss}). % The flexibility comes at the price that the method has to be finely tuned for the data set because some parameter combinations are simply unsuitable for certain data. % The method is not suitable for very large data sets, because memory scales with $\mathcal{O}(n^2)$ and computation time with $\mathcal{O}(n^3)$. % Diffusion Maps, Isomap, Locally Linear Embedding, and some other techniques can be seen as special cases of kPCA. In which case, an out-of-sample extension using the Nyström formula can be applied \citep{bengio_learning_2004}. % This can also yield applications for bigger data, where an embedding is trained with a sub-sample of all data and then the data is embedded using the Nyström formula. Kernel PCA in R is implemented in the \CRANpkg{kernlab} package using the function \code{kernlab::kpca}, and supports a number of kernels and user defined functions. For details see the help page for \code{kernlab::kpca}. The \pkg{dimRed} package wraps \code{kernlab::kpca} but additionally provides forward and inverse methods \citep{bakir_learning_2004} which can be used to fit out-of-sample data or to visualize the transformation of the data space. % \subsection{Classical Scaling} \label{sec:classscale} What today is called Classical Scaling was first introduced by \citet{torgerson_multidimensional_1952}. It uses an eigenvalue decomposition of a transformed distance matrix to find an embedding that maintains the distances of the distance matrix. % The method works because of the same reason that kPCA works, i.e.,\ classical scaling can be seen as a kPCA with kernel $x^Ty$. % A matrix of Euclidean distances can be transformed into an inner product matrix by some simple transformations and therefore yields the same result as a PCA\@. % Classical scaling is conceptually more general than PCA in that arbitrary distance matrices can be used, i.e.,\ the method does not even need the original coordinates, just a distance matrix $D$. % Then it tries to find an embedding $Y$ so that $\hat d_{ij}$ is as similar to $d_{ij}$ as possible. The disadvantage is that it is computationally much more demanding, i.e.,\ an eigenvalue decomposition of an $n\times n$ matrix has to be computed. This step requires $\mathcal{O}(n^2)$ memory and $\mathcal{O}(n^3)$ computation time, while PCA requires only the eigenvalue decomposition of a $d\times d$ matrix and usually $n \gg d$. % R implements classical scaling in the \code{cmdscale} function. % The \pkg{dimRed} package wraps \code{cmdscale} and allows the specification of arbitrary distance functions for calculating the distance matrix. Additionally a forward method is implemented. \subsection{Isomap} \label{sec:isomap} As Classical Scaling can deal with arbitrarily defined distances, \citet{tenenbaum_global_2000} suggested to approximate the structure of the manifold by using geodesic distances. % In practice, a graph is created by either keeping only the connections between every point and its $k$ nearest neighbors to produce a $k$-nearest neighbor graph ($k$-NNG), or simply by keeping all distances smaller than a value $\varepsilon$ producing an $\varepsilon$-neighborhood graph ($\varepsilon$-NNG). % Geodesic distances are obtained by recording the distance on the graph and classical scaling is used to find an embedding in fewer dimensions. This leads to an ``unfolding'' of possibly convoluted structures (see Figure~\ref{fig:knn}). Isomap's computational cost is dominated by the eigenvalue decomposition and therefore scales with $\mathcal{O}(n^3)$. % Other related techniques can use more efficient algorithms because the distance matrix becomes sparse due to a different preprocessing. In R, Isomap is implemented in the \CRANpkg{vegan} package. The \code{vegan::isomap} calculates an Isomap embedding and \code{vegan::isomapdist} calculates a geodesic distance matrix. % The \pkg{dimRed} package uses its own implementation. This implementation is faster mainly due to using a KD-tree for the nearest neighbor search (from the \CRANpkg{RANN} package) and to a faster implementation for the shortest path search in the $k$-NNG (from the \CRANpkg{igraph} package). % The implementation in \pkg{dimRed} also includes a forward method that can be used to train the embedding on a subset of data points and then use these points to approximate an embedding for the remaining points. This technique is generally referred to as landmark Isomap \citep{de_silva_sparse_2004}. % \subsection{Locally Linear Embedding} \label{sec:lle} Points that lie on a manifold in a high dimensional space can be reconstructed through linear combinations of their neighborhoods if the manifold is well sampled and the neighbohoods lie on a locally linear patch. % These reconstruction weights, $W$, are the same in the high dimensional space as the internal coordinates of the manifold. % Locally Linear Embedding \citep[LLE; ][]{roweis_nonlinear_2000} is a technique that constructs a weight matrix $W \in \mathbb{R}^{n\times n}$ with elements $w_{ij}$ so that \begin{equation} \sum_{i=1}^n \bigg\| x_i- \sum_{j=1}^{n} w_{ij}x_j \bigg\|^2\label{eq:lle} \end{equation} is minimized under the constraint that $w_{ij} = 0 $ if $x_j$ does not belong to the neighborhood and the constraint that $\sum_{j=1}^n w_{ij} = 1$. % Finally the embedding is made in such a way that the following cost function is minimized for $Y$, \begin{equation} \sum_{i=1}^n\bigg\| y_i - \sum_{j=1}^n w_{ij}y_j \bigg\|^2.\label{eq:lle2} \end{equation} This can be solved using an eigenvalue decomposition. Conceptually the method is similar to Isomap but it is computationally much nicer because the weight matrix is sparse and there exist efficient solvers. % In R, LLE is implemented by the package \CRANpkg{lle}, the embedding can be calculated with \code{lle::lle}. Unfortunately the implementation does not make use of the sparsity of the weight matrix $W$. % The manifold must be well sampled and the neighborhood size must be chosen appropriately for LLE to give good results. % \subsection{Laplacian Eigenmaps} \label{sec:laplaceigenmaps} Laplacian Eigenmaps were originally developed under the name spectral clustering to separate non-convex clusters. % Later it was also used for graph embedding and DR \citep{belkin_laplacian_2003}. % A number of variants have been proposed. % First, a graph is constructed, usually from a distance matrix, the graph can be made sparse by keeping only the $k$ nearest neighbors, or by specifying an $\varepsilon$ neighborhood. % Then, a similarity matrix $W$ is calculated by using a Gaussian kernel (see Equation \ref{eq:gauss}), if $c = 2 \sigma^2 = \infty$, then all distances are treated equally, the smaller $c$ the more emphasis is given to differences in distance. % The degree of vertex $i$ is $d_i = \sum_{j=1}^n w_{ij}$ and the degree matrix, $D$, is the diagonal matrix with entries $d_i$. % Then we can form the graph Laplacian $L = D - W$ and, then, there are several ways how to proceed, an overview can be found in \citet{luxburg_tutorial_2007}. % The \pkg{dimRed} package implements the algorithm from \citet{belkin_laplacian_2003}. Analogously to LLE, Laplacian eigenmaps avoid computational complexity by creating a sparse matrix and not having to estimate the distances between all pairs of points. % Then the eigenvectors corresponding to the lowest eigenvalues larger than $0$ of either the matrix $L$ or the normalized Laplacian $D^{-1/2}LD^{-1/2}$ are computed and form the embedding. \subsection{Diffusion Maps} \label{sec:isodiffmaplle} Diffusion Maps \citep{coifman_diffusion_2006} take a distance matrix as input and calculates the transition probability matrix $P$ of a diffusion process between the points to approximate the manifold. % Then the embedding is done by an eigenvalue decompositon of $P$ to calculate the coordinates of the embedding. % The algorithm for calculating Diffusion Maps shares some elements with the way Laplacian Eigenmaps are calculated. % Both algorithms depart from the same weight matrix, Diffusion Maps calculate the transition probability on the graph after $t$ time steps and do the embedding on this probability matrix. The idea is to simulate a diffusion process between the nodes of the graph, which is more robust to short-circuiting than the $k$-NNG from Isomap (see bottom right Figure \ref{fig:knn}). % Diffusion maps in R are accessible via the \code{diffusionMap::diffuse()} function, which is available in the \CRANpkg{diffusionMap} package. % Additional points can be approximated into an existing embedding using the Nyström formula \citep{bengio_learning_2004}. % The implementation in \pkg{dimRed} is based on the \code{diffusionMap::diffuse} function. % , which does not contain an % approximation for unequally sampled manifolds % \citep{coifman_geometric_2005}. % \subsection{non-Metric Dimensional Scaling} \label{sec:nmds} While Classical Scaling and derived methods (see section \nameref{sec:classscale}) use eigenvector decomposition to embed the data in such a way that the given distances are maintained, non-Metric Dimensional Scaling \citep[nMDS, ][]{kruskal_multidimensional_1964,kruskal_nonmetric_1964} uses optimization methods to reach the same goal. % Therefore a stress function, \begin{equation} \label{eq:stress} S = \sqrt{\frac{\sum_{i>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { library(dimRed); library(ggplot2); #library(dplyr); library(tidyr) ## define which methods to apply embed_methods <- c("Isomap", "PCA") ## load test data set data_set <- loadDataSet("3D S Curve", n = 1000) ## apply dimensionality reduction data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) names(data_emb) <- embed_methods ## plot data set, embeddings, and quality analysis ## plot(data_set, type = "3vars") ## lapply(data_emb, plot, type = "2vars") ## plot_R_NX(data_emb) add_label <- function(label) grid::grid.text(label, 0.2, 1, hjust = 0, vjust = 1, gp = grid::gpar(fontface = "bold", cex = 1.5)) ## pdf('~/phd/text/dimRedPackage/plots/plot_example.pdf', width = 4, height = 4) ## plot the results plot(data_set, type = "3vars", angle = 15, mar = c(3, 3, 0, 0), box = FALSE, grid = FALSE, pch = 16) add_label("a") par(mar = c(4, 4, 0, 0) + 0.1, bty = "n", las = 1) plot(data_emb$Isomap, type = "2vars", pch = 16) add_label("b") plot(data_emb$PCA, type = "2vars", pch = 16) add_label("d") ## calculate quality scores print( plot_R_NX(data_emb) + theme(legend.title = element_blank(), legend.position = c(0.5, 0.1), legend.justification = c(0.5, 0.1)) ) add_label("c") } else { # These cannot all be plot(1:10)!!! It's a mistery to me. plot(1:10) barplot(1:10) hist(1:10) plot(1:10) } @ \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-1.pdf} \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-2.pdf} \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-3.pdf} \includegraphics[page=1,width=.45\textwidth]{figure/pca_isomap_example-4.pdf} \caption[dimRed example]{% Comparing PCA and Isomap: % (a) An S-shaped manifold, colors represent the internal coordinates of the manifold. % (b) Isomap embedding, the S-shaped manifold is unfolded. % (c) $R_{NX}$ plotted agains neighborhood sizes, Isomap is much better at preserving local distances and PCA is better at preserving global Euclidean distances. % The numbers on the legend are the $\text{AUC}_{1 / K}$. (d) PCA projection of the data, the directions of maximum variance are preserved. % }\label{fig:plotexample} \end{figure} <>= ## define which methods to apply embed_methods <- c("Isomap", "PCA") ## load test data set data_set <- loadDataSet("3D S Curve", n = 1000) ## apply dimensionality reduction data_emb <- lapply(embed_methods, function(x) embed(data_set, x)) names(data_emb) <- embed_methods ## figure \ref{fig:plotexample}a, the data set plot(data_set, type = "3vars") ## figures \ref{fig:plotexample}b (Isomap) and \ref{fig:plotexample}d (PCA) lapply(data_emb, plot, type = "2vars") ## figure \ref{fig:plotexample}c, quality analysis plot_R_NX(data_emb) @ The function \code{plot\_R\_NX} produces a figure that plots the neighborhood size ($k$ at a log-scale) against the quality measure $\text{R}_{NX}(k)$ (see Equation \ref{eq:rnx}). % This gives an overview of the general behavior of methods: if $\text{R}_{NX}$ is high for low values of $K$, then local neighborhoods are maintained well; if $\text{R}_{NX}$ is high for large values of $K$, then global gradients are maintained well. % It also provides a way to directly compare methods by plotting more than one $\text{R}_{NX}$ curve and an overall quality of the embedding by taking the area under the curve as an indicator for the overall quality of the embedding (see fig~\ref{eq:auclnk}) which is shown as a number in the legend. Therefore we can see from Figure~\ref{fig:plotexample}c that $t$-SNE is very good a maintaining close and medium distances for the given data set, whereas PCA is only better at maintaining the very large distances. % The large distances are dominated by the overall bent shape of the S in 3D space, while the close distances are not affected by this bending. % This is reflected in the properties recovered by the different methods, the PCA embedding recovers the S-shape, while $t$-SNE ignores the S-shape and recovers the inner structure of the manifold. % Example 2: Often the quality of an embedding strongly depends on the choice of parameters, the interface of \pkg{dimRed} can be used to facilitate searching the parameter space. Isomap has one parameter $k$ which determines the number of neighbors used to construct the $k$-NNG\@. % If this number is too large, then Isomap will resemble an MDS (Figure~\ref{fig:knn} e), if the number is too small, the resulting embedding contains holes (Figure~\ref{fig:knn} c). % The following code finds the optimal value, $k_{\text{max}}$, for $k$ using the $Q_{\text{local}}$ criterion, the results are visualized in Figure~\ref{fig:knn} a: \begin{figure}[htp] \centering <>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { library(dimRed) library(cccd) ## Load data ss <- loadDataSet("3D S Curve", n = 500) ## Parameter space kk <- floor(seq(5, 100, length.out = 40)) ## Embedding over parameter space emb <- lapply(kk, function(x) embed(ss, "Isomap", knn = x)) ## Quality over embeddings qual <- sapply(emb, function(x) quality(x, "Q_local")) ## Find best value for K ind_max <- which.max(qual) k_max <- kk[ind_max] add_label <- function(label){ par(xpd = TRUE) b = par("usr") text(b[1], b[4], label, adj = c(0, 1), cex = 1.5, font = 2) par(xpd = FALSE) } names(qual) <- kk } @ <<"select_k",include=FALSE,fig.width=11,fig.height=5>>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { par(mfrow = c(1, 2), mar = c(5, 4, 0, 0) + 0.1, oma = c(0, 0, 0, 0)) plot(kk, qual, type = "l", xlab = "k", ylab = expression(Q[local]), bty = "n") abline(v = k_max, col = "red") add_label("a") plot(ss, type = "3vars", angle = 15, mar = c(3, 3, 0, 0), box = FALSE, grid = FALSE, pch = 16) add_label("b") } else { plot(1:10) plot(1:10) } @ <<"knngraphs",include=FALSE,fig.width=8,fig.height=3>>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { par(mfrow = c(1, 3), mar = c(5, 4, 0, 0) + 0.1, oma = c(0, 0, 0, 0)) add_knn_graph <- function(ind) { nn1 <- nng(ss@data, k = kk[ind]) el <- get.edgelist(nn1) segments(x0 = emb[[ind]]@data@data[el[, 1], 1], y0 = emb[[ind]]@data@data[el[, 1], 2], x1 = emb[[ind]]@data@data[el[, 2], 1], y1 = emb[[ind]]@data@data[el[, 2], 2], col = "#00000010") } plot(emb[[2]]@data@data, type = "n", bty = "n") add_knn_graph(2) points(emb[[2]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("c") plot(emb[[ind_max]]@data@data, type = "n", bty = "n") add_knn_graph(ind_max) points(emb[[ind_max]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("d") plot(emb[[length(emb)]]@data@data, type = "n", bty = "n") add_knn_graph(length(emb)) points(emb[[length(emb)]]@data@data, col = dimRed:::colorize(ss@meta), pch = 16) add_label("e") } else { plot(1:10) plot(1:10) plot(1:10) } @ \includegraphics[width=.95\textwidth]{figure/select_k-1.pdf} \includegraphics[width=.95\textwidth]{figure/knngraphs-1.pdf} \caption[estimating $k$ using @Q_\text{local}]{% Using \pkg{dimRed} and the $Q_\text{local}$ indicator to estimate a good value for the parameter $k$ in Isomap. % (a) $Q_\text{local}$ for different values of $k$, the vertical red line indicates the maximum $k_{\text{max}}$. % (b) The original data set, a 2 dimensional manifold bent in an S-shape in 3 dimensional space. % Bottom row: Embeddings and $k$-NNG for different values of $k$. % (c) When $k = 5$, the value for $k$ is too small resulting in holes in the embedding, the manifold itself is still unfolded correctly. % (d) Choose $k = k_\text{max}$, the best representation of the original manifold in two dimensions achievable with Isomap. % (e) $k = 100$, too large, the $k$-NNG does not approximate the manifold any more. % }\label{fig:knn} \end{figure} <>= ## Load data ss <- loadDataSet("3D S Curve", n = 500) ## Parameter space kk <- floor(seq(5, 100, length.out = 40)) ## Embedding over parameter space emb <- lapply(kk, function(x) embed(ss, "Isomap", knn = x)) ## Quality over embeddings qual <- sapply(emb, function(x) quality(x, "Q_local")) ## Find best value for K ind_max <- which.max(qual) k_max <- kk[ind_max] @ Figure~\ref{fig:knn}a shows how the $Q_{\text{local}}$ criterion changes when varying the neighborhood size $k$ for Isomap, the gray lines in Figure~\ref{fig:knn} represent the edges of the $k$-NN Graph. % If the value for $k$ is too low, the inner structure of the manifold will still be recovered, but it will be imperfect (Figure~\ref{fig:knn}c, note that the holes appear in places that are not covered by the edges of the $k$-NN Graph), therefore the $Q_{\text{local}}$ score is lower than optimal. % If $k$ is too large, the error of the embedding is much larger due to short circuiting and we observe a very steep drop in the $Q_{\text{local}}$ score. % The short circuiting can be observed in Figure~\ref{fig:knn}e with the edges that cross the gap between the tips and the center of the S-shape. % % Example 3: It is also very easy to compare across methods and quality scores. % The following code produces a matrix of quality scores and methods, where \code{dimRedMethodList} returns a character vector with all methods. A visualization of the matrix can be found in Figure~\ref{fig:qualityexample}. % \begin{figure}[htp] \centering <<"plot_quality",include=FALSE>>= if(Sys.getenv("BNET_BUILD_VIGNETTE") != "") { embed_methods <- dimRedMethodList() quality_methods <- c("Q_local", "Q_global", "AUC_lnK_R_NX", "cophenetic_correlation") iris_data <- loadDataSet("Iris") quality_results <- matrix( NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods) ) embedded_data <- list() for (e in embed_methods) { try(embedded_data[[e]] <- embed(iris_data, e)) for (q in quality_methods) try(quality_results[e,q] <- quality(embedded_data[[e]], q)) } quality_results <- quality_results[order(rowMeans(quality_results)), ] palette(c("#1b9e77", "#d95f02", "#7570b3", "#e7298a", "#66a61e")) col_hsv <- rgb2hsv(col2rgb(palette())) ## col_hsv["v", ] <- col_hsv["v", ] * 3 / 1 palette(hsv(col_hsv["h",], col_hsv["s",], col_hsv["v",])) par(mar = c(2, 8, 0, 0) + 0.1) barplot(t(quality_results), beside = TRUE, col = 1:4, legend.text = quality_methods, horiz = TRUE, las = 1, cex.names = 0.85, args.legend = list(x = "topleft", bg = "white", cex = 0.8)) } else { plot(1:10) } @ \includegraphics[width=.5\textwidth]{figure/plot_quality-1.pdf} \caption[Quality comparision]{% A visualization of the \code{quality\_results} matrix. % The methods are ordered by mean quality score. % The reconstruction error was omitted, because a higher value means a worse embedding, while in the present methods a higher score means a better embedding. % Parameters were not tuned for the example, therefore it should not be seen as a general quality assessment of the methods. % }\label{fig:qualityexample} \end{figure} <>= embed_methods <- dimRedMethodList() quality_methods <- c("Q_local", "Q_global", "AUC_lnK_R_NX", "cophenetic_correlation") scurve <- loadDataSet("3D S Curve", n = 2000) quality_results <- matrix( NA, length(embed_methods), length(quality_methods), dimnames = list(embed_methods, quality_methods) ) embedded_data <- list() for (e in embed_methods) { embedded_data[[e]] <- embed(scurve, e) for (q in quality_methods) try(quality_results[e, q] <- quality(embedded_data[[e]], q)) } @ This example showcases the simplicity with which different methods and quality criteria can be combined. % Because of the strong dependencies on parameters it is not advised to apply this kind of analysis without tuning the parameters for each method separately. % There is no automatized way to tune parameters in \pkg{dimRed}. % \section{Conclusion} \label{sec:conc} This paper presents the \pkg{dimRed} and \pkg{coRanking} packages and it provides a brief overview of the methods implemented therein. % The \pkg{dimRed} package is written in the R language, one of the most popular languages for data analysis. The package is freely available from CRAN. % The package is object oriented and completely open source and therefore easily available and extensible. % Although most of the DR methods already had implementations in R, \pkg{dimRed} adds some new methods for dimensionality reduction, and \pkg{coRanking} adds methods for an independent quality control of DR methods to the R ecosystem. % DR is a widely used technique. However, due to the lack of easily usable tools, choosing the right method for DR is complex and depends upon a variety of factors. % The \pkg{dimRed} package aims to facilitate experimentation with different techniques, parameters, and quality measures so that choosing the right method becomes easier. % The \pkg{dimRed} package wants to enable the user to objectively compare methods that rely on very different algorithmic approaches. % It makes the life of the programmer easier, because all methods are aggregated in one place and there is a single interface and standardized classes to access the functionality. % \section{Acknowledgments} \label{sec:ack} We thank Dr.\ G.\ Camps-Valls and an anonymous reviewer for many useful comments. % This study was supported by the European Space Agency (ESA) via the Earth System Data Lab project (\url{http://earthsystemdatacube.org}) and the EU via the H2020 project BACI, grant agreement No 640176. % \bibliographystyle{abbrvnat} \bibliography{bibliography} \end{document} dimRed/inst/doc/dimensionality-reduction.pdf0000644000176200001440000344127014153220135020724 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 5004 /Filter /FlateDecode /N 95 /First 794 >> stream x\kwF&99B_sQ;qdgx?P$(!Hlg~n/Y&%iYꮺ}AYBB \ L a+/tW[[Yd!TEP`KRaU!BaRqa!EaPYU 40h,}Me[x($%$l}U8CיyQ ';I_kL CY^ (}YCQEf4cmRh9 $Y̱q6P iRJCmd驥 Yq9 +Ѝ4a!֢h6h'Hւ.d!YndMj!Y{d*6GBw jYHB9H:H@{S0C3Pϓ84dG!CWt =yWA $+A N,u. 5 .4зE7q}uUh2FmI~fj"q ;:*#\?[D\u狦KiQW/G]U|KA ϶\}8[tzUͤ2-&YL}iqS_vE()9.yqu[5ėu7h+hq5(5VPv<2~.[o 6wOtY:OǕIQp?&9"R2#|ё,&Kyw7)L!s,E \ =TcȁܐY_TD珏kV^"uvEէ#lO󝏫5L +9pg~5?2!2_Os<`$qҶJmǫ&GmzˣWϾzq| |"{O2!/ ;K#jxw?kHkk Tt LLti >3O`kx7C]C8x: B)ҌG'LJQ{ן#;6y J&V؏FҶqI#%LDٱכٸtRN 7 g (Վ)y?߅n|a#}ˎw '=eGN ~aد5Svڌլvi!lƋb/.Fl*VWj>lʦf߻Mgl cga;fu79ͻz6؂!ԫj-p]D}VaU~g_0bcUYIwĽta-k:V`[`XwT/O/c7w,HҰAiH8gm7q=6>7atQ]O073.vm x|!몋Q[Ǐx \psom!9їל-91tDOF-7|8l 0{ޡAtj7ɴ0[:J*9|;'D1[Y"ޖ.)rIfű󷽢Dn1JjrD>2)lj̅]pgHW܉p$w?¹/(^%kKwނ 7^E2yeL SQSLIW/@iK>CRى9epEk8U%N$ .5jLJSEAᛠ?M}M^FqoP2?Fomv!م]x)M\Cz.iG 7B uŮ5Og!ڿrAnV0r2-yr |A&EdvSH59T>SA;;!ʓգgϞU81[p·>ZfN` a5v؎ٛd)#ҹ ,CJ[.tCF:sWy )O]5 c䪋>FRmB0f\|1ue99/Qⲭ 5 ގ./Gtm Cp^p{Oޯ3$eHgw 7b!@' ~"oO`,%F "9PI+%U)%^Fa) K3)%,n5*v y %ߟ ^+%ert3lbin4׀RxNCICICICI-&I#I$7IMRfdw쭸[_r$DsKMa;j嶵1-ZKQQA)\xZťw]Rʥw}x:>'5>IIJ.zo.kd<ߦ>pSJ8 Ei)P1)R- ϠIX_$T9 %E= cWKAA_ SZ-iJҎ擖bn'Rao9~hr%rNݶ *O)u x^'#tcYYɔٔ ؼ!rvˏ=lˍyjJoqOGƕܜ5et>k?{~ֶ4><2s󓞶YY̊Vv\S9^YfW؈k+o?6Con8)߯FzF'&j{Vq&s6:4#돩tr?2y6#ѧ a8Z15MMzhVR`{@@ví*Ena\TyY!=^je꺡_] *VZR?[+-\㊸ȜןK) Ul2aae｜ R~^jեC'ɉDISg.Ў|ryR,O"ȹɣ٣ ۵qZrgV?'>!9Jo8j}/]2f\E!غ4QNtc"V;XqT!w.ՂէiiYo|IWޚMtQU4A+KJˊxh}j2 ',SjT$Kt>EՈebɮRKsgoM<p3 M^%UG7VUWhz$F㋂|d@11t;cv4fmy34/,X#%bK/u/cT5*@{Y ZxiYE㼤Yݠl51 p" %9լ>-'T{/=mOa;z9B$弾l82PQw4F B[M販 Z\^NXDAz>i@w,,HQb-(ғf:jC9Y9ˑ !8 . ~-}˒`inג{1t8k䎔{'[}UovffnBgLi'&_V-hfJ8poWe5)&  pvYV9?CKG\z~`dsޡ VᴮSѰ9\X#Ɛ!9RwJNt9ZRݚo$Z낲]=>SRwhjBՎ@*wi=MO+Dl:PP {`NTWq5(*a&2xs0lr~:jT\xv#>*0bՇ!7мIrU ^S&՟Ǥ/%-q*{ e{ 3靍{x̥ȳ>FhIX(y4UqyҠ %UWH^ f$lZ,i4I|qC%_Y?Kv ȷTB5L}yg0iZz@#F&b&4F O%2 2icSƢa û0Nwl%{*LB'uʥm 4d,bPyWHonVyxGt֧z[~4i&u5UWM`UӂV5UwJ*=b&mtA> z?)ZCa;*rf(Abtp3c8gR[ny7ħ!1qw`o")^w[m p{ls Y:h߇ln`L)vMvw8ZutZ5bmdNI[ Ez7ȯGP]kz155jyMTӛjiE4Zbgpk=3ڮ劕ǡZpYendstream endobj 97 0 obj << /Subtype /XML /Type /Metadata /Length 1387 >> stream GPL Ghostscript 9.55.0 2021-12-05T21:26:03+01:00 2021-12-05T21:26:03+01:00 LaTeX with hyperref endstream endobj 98 0 obj << /Type /ObjStm /Length 4623 /Filter /FlateDecode /N 95 /First 900 >> stream x\ksF~>V*ޭd;q98rR( PBR_}EbAx fzzkzR&3%*3QYg^::,%Li.@6t3,^Lk"fE)ӑjRJfF:*Z]̸Du(+e3kU\fGY$d6j\&~2D@h9q34 6s1Kz/=wS'fޣu"Gndf<}ntEmfc/㲘<}n|Tī%PO̒ SXFYHFFW`i@h@&~>1,Qn8P&wN[w=I Tr}#R9$`DWgQ33ޡ`XeFM$(=@q qtG#q_'.pU@;؀vt7?tDA/$'0pUDMqMG0f1oA5q;;?h)| jL?w~^e_T4+r~ m=z^b>>)VTxy&VT?Io TuYmXʳYUꆳUg[˻Ec%rU\-_uWU|-_uWe~wOK;- \xxrꛯNx6'K-|XF$X|K}? 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"*,H]PQ{([/A/Np>-C6 Li/0y&:Bf~t컛*~tO33`䆀 2gLv&(_nendstream endobj 463 0 obj << /Type /XRef /Length 336 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Info 3 0 R /Root 2 0 R /Size 464 /ID [<6c14cf8161e1d4021994aeddb6565ab1>] >> stream x햿/CQϽ-m1a1I1t1 j5,!Z.Dbbb|wu>1Ƈ_U&C-+E%"jR6?gxVsm~,+Kd_)ɲS㉝,fzDʒغ,6|̓bI-JgX' >ԧ{<Ԫ6137nb,ksw)tn̙Awp'҂!nbTbL΋ۼ1=bnGSK'guS9y}`>E endstream endobj startxref 933973 %%EOF dimRed/inst/CITATION0000644000176200001440000000105313371631672013600 0ustar liggesusersbibentry(bibtype = "Article", author = c(person("Guido", "Kraemer"), person("Markus", "Reichstein"), person("Miguel", "D.", "Mahecha")), title = "{dimRed} and {coRanking}---Unifying Dimensionality Reduction in R", year = "2018", journal = "The R Journal", url = "https://journal.r-project.org/archive/2018/RJ-2018-039/index.html", pages = "342--358", volume = "10", number = "1", note = sprintf("coRanking version %s", meta$Version))