Introduction
R package corrplot provides a visual exploratory
tool on correlation matrix that supports automatic variable reordering
to help detect hidden patterns among variables.
corrplot is very easy to use and provides a rich array of plotting
options in visualization method, graphic layout, color, legend, text
labels, etc. It also provides p-values and confidence intervals to help
users determine the statistical significance of the correlations.
corrplot() has about 50 parameters, however the mostly
common ones are only a few. We can get a correlation matrix plot with
only one line of code in most scenes.
The mostly using parameters include method,
type, order, diag, and etc.
There are seven visualization methods (parameter method)
in corrplot package, named 'circle', 'square',
'ellipse', 'number', 'shade',
'color', 'pie'. Color intensity of the glyph
is proportional to the correlation coefficients by default color
setting.
'circle' and 'square', the
areas of circles or squares show the absolute value of
corresponding correlation coefficients.
'ellipse', the ellipses have their eccentricity
parametrically scaled to the correlation value. It comes from D.J.
Murdoch and E.D. Chow’s job, see in section References.
'number', coefficients numbers with different
color.
'color', square of equal size with different
color.
'shade', similar to 'color', but the
negative coefficients glyphs are shaded. Method 'pie' and
'shade' come from Michael Friendly’s job.
'pie', the circles are filled clockwise for positive
values, anti-clockwise for negative values.
corrplot.mixed() is a wrapped function for mixed
visualization style, which can set the visual methods of lower and upper
triangular separately.
There are three layout types (parameter type):
'full', 'upper' and 'lower'.
The correlation matrix can be reordered according to the correlation
matrix coefficients. This is important to identify the hidden structure
and pattern in the matrix.
## corrplot 0.95 loaded
M = cor(mtcars)
corrplot(M, method = 'number') # colorful number
corrplot(M, method = 'color', order = 'alphabet')
corrplot(M) # by default, method = 'circle'
corrplot(M, order = 'AOE') # after 'AOE' reorder
corrplot(M, method = 'shade', order = 'AOE', diag = FALSE)
corrplot(M, method = 'square', order = 'FPC', type = 'lower', diag = FALSE)
corrplot(M, method = 'ellipse', order = 'AOE', type = 'upper')
corrplot.mixed(M, order = 'AOE')
corrplot.mixed(M, lower = 'shade', upper = 'pie', order = 'hclust')
Reorder a correlation matrix
The details of four order algorithms, named
'AOE', 'FPC', 'hclust',
'alphabet' are as following.
'AOE' is for the angular order of the eigenvectors.
It is calculated from the order of the angles \(a_i\),
\[
a_i =
\begin{cases}
\arctan (e_{i2}/e_{i1}), & \text{if $e_{i1}>0$;}
\newline
\arctan (e_{i2}/e_{i1}) + \pi, & \text{otherwise.}
\end{cases}
\]
where \(e_1\) and \(e_2\) are the largest two eigenvalues of
the correlation matrix. See Michael Friendly
(2002) for details.
'FPC' for the first principal component
order.
'hclust' for hierarchical clustering order, and
'hclust.method' for the agglomeration method to be used.
'hclust.method' should be one of 'ward',
'ward.D', 'ward.D2', 'single',
'complete', 'average',
'mcquitty', 'median' or
'centroid'.
'alphabet' for alphabetical order.
You can also reorder the matrix ‘manually’ via function
corrMatOrder().
If using 'hclust', corrplot() can draw
rectangles around the plot of correlation matrix based on the results of
hierarchical clustering.
corrplot(M, order = 'hclust', addrect = 2)
corrplot(M, method = 'square', diag = FALSE, order = 'hclust',
addrect = 3, rect.col = 'blue', rect.lwd = 3, tl.pos = 'd')
R package seriation provides the infrastructure for
ordering objects with an implementation of several
seriation/sequencing/ordination techniques to reorder matrices,
dissimilarity matrices, and dendrograms. For more information, see in
section References.
We can reorder the matrix via seriation package and
then corrplot it. Here are some examples.
library(seriation)
list_seriation_methods('matrix')
## [1] "AOE" "BEA" "BEA_TSP" "CA" "Heatmap" "Identity"
## [7] "LLE" "Mean" "PCA" "PCA_angle" "Random" "Reverse"
list_seriation_methods('dist')
## [1] "ARSA" "BBURCG" "BBWRCG" "Enumerate"
## [5] "GSA" "GW" "GW_average" "GW_complete"
## [9] "GW_single" "GW_ward" "HC" "HC_average"
## [13] "HC_complete" "HC_single" "HC_ward" "Identity"
## [17] "MDS" "MDS_angle" "OLO" "OLO_average"
## [21] "OLO_complete" "OLO_single" "OLO_ward" "QAP_2SUM"
## [25] "QAP_BAR" "QAP_Inertia" "QAP_LS" "R2E"
## [29] "Random" "Reverse" "SGD" "SPIN_NH"
## [33] "SPIN_STS" "Sammon_mapping" "Spectral" "Spectral_norm"
## [37] "TSP" "VAT" "isoMDS" "isomap"
## [41] "metaMDS" "monoMDS"
data(Zoo)
Z = cor(Zoo[, -c(15, 17)])
dist2order = function(corr, method, ...) {
d_corr = as.dist(1 - corr)
s = seriate(d_corr, method = method, ...)
i = get_order(s)
return(i)
}
Methods 'PCA_angle' and 'HC' in
seriation, are same as 'AOE' and
'hclust' separately in corrplot() and
corrMatOrder().
Here are some plots after seriation.
# Fast Optimal Leaf Ordering for Hierarchical Clustering
i = dist2order(Z, 'OLO')
corrplot(Z[i, i], cl.pos = 'n')
# Quadratic Assignment Problem
i = dist2order(Z, 'QAP_2SUM')
corrplot(Z[i, i], cl.pos = 'n')
# Multidimensional Scaling
i = dist2order(Z, 'MDS_nonmetric')
## Warning in get_seriation_method("dist", method): seriation method
## 'MDS_nonmetric' is now deprecated and will be removed in future releases. Using
## `isoMDS`
corrplot(Z[i, i], cl.pos = 'n')
# Simulated annealing
i = dist2order(Z, 'ARSA')
corrplot(Z[i, i], cl.pos = 'n')
# TSP solver
i = dist2order(Z, 'TSP')
corrplot(Z[i, i], cl.pos = 'n')
# Spectral seriation
i = dist2order(Z, 'Spectral')
corrplot(Z[i, i], cl.pos = 'n')
corrRect() can add rectangles on the plot with three
ways(parameter index, name and
namesMat) after corrplot(). We can use pipe
operator *>% in package magrittr with more
convenience. Since R 4.1.0, |> is supported without
extra package.
library(magrittr)
# Rank-two ellipse seriation, use index parameter
i = dist2order(Z, 'R2E')
corrplot(Z[i, i], cl.pos = 'n') %>% corrRect(c(1, 9, 15))
# use name parameter
# Since R 4.1.0, the following one line code works:
# corrplot(M, order = 'AOE') |> corrRect(name = c('gear', 'wt', 'carb'))
corrplot(Z, order = 'AOE') %>%
corrRect(name = c('tail', 'airborne', 'venomous', 'predator'))
# use namesMat parameter
r = rbind(c('eggs', 'catsize', 'airborne', 'milk'),
c('catsize', 'eggs', 'milk', 'airborne'))
corrplot(Z, order = 'hclust') %>% corrRect(namesMat = r)
Change color spectra, color-legend and text-legend
We can get sequential and diverging colors from COL1()
and COL2(). The color palettes are borrowed from
RColorBrewer package.
Notice: the middle color getting from
COL2() is fixed to '#FFFFFF'(white), thus we
can visualizing element 0 with white color.
COL1(): Get sequential colors, suitable for visualize a
non-negative or non-positive matrix (e.g. matrix in [0, 20], or [-100,
-10], or [100, 500]).COL2(): Get diverging colors, suitable for visualize a
matrix which elements are partly positive and partly negative
(e.g. correlation matrix in [-1, 1], or [-20, 100]).
The colors of the correlation plots can be customized by
col in corrplot(). They are distributed
uniformly in col.lim interval.
col: vector, the colors of glyphs. They are distributed
uniformly in col.lim interval. By default,
- If
is.corr is TRUE, col will
be COL2('RdBu', 200).
- If
is.corr is FALSE,
- and
corr is a non-negative or non-positive matrix,
col will be COL1('YlOrBr', 200);
- otherwise (elements are partly positive and partly negative),
col will be COL2('RdBu', 200).
col.lim: the limits (x1, x2) interval for assigning
color by col. By default,
col.lim will be c(-1, 1) when
is.corr is TRUE,col.lim will be c(min(corr), max(corr))
when is.corr is FALSE.- NOTICE: if you set
col.lim when
is.corr is TRUE, the assigning colors are
still distributed uniformly in [-1, 1], it only affect the display on
color-legend.
is.corr: logical, whether the input matrix is a
correlation matrix or not. The default value is TRUE. We
can visualize a non-correlation matrix by setting
is.corr = FALSE.
Here all diverging colors from COL2() and sequential
colors from COL1() are shown below.
Diverging colors:
Sequential colors:
Usage of COL1() and COL2():
COL1(sequential = c("Oranges", "Purples", "Reds", "Blues", "Greens",
"Greys", "OrRd", "YlOrRd", "YlOrBr", "YlGn"), n = 200)
COL2(diverging = c("RdBu", "BrBG", "PiYG", "PRGn", "PuOr", "RdYlBu"), n = 200)
In addition, function colorRampPalette() is very
convenient for generating color spectrum.
Parameters group cl.* is for color-legend. The
common-using are:
cl.pos is for the position of color labels. It is
character or logical. If character, it must be one of 'r'
(means right, default if type='upper' or
'full'), 'b' (means bottom, default if
type='lower') or 'n'(means don’t draw
color-label).cl.ratio is to justify the width of color-legend,
0.1~0.2 is suggested.
Parameters group tl.* is for text-legend. The
common-using are:
tl.pos is for the position of text labels. It is
character or logical. If character, it must be one of 'lt',
'ld', 'td', 'd', 'l'
or 'n'. 'lt'(default if
type='full') means left and top, 'ld'(default
if type='lower') means left and diagonal,
'td'(default if type='upper') means top and
diagonal(near), 'd' means diagonal, 'l' means
left, 'n' means don’t add text-label.tl.cex is for the size of text label (variable
names).tl.srt is for text label string rotation in
degrees.
corrplot(M, order = 'AOE', col = COL2('RdBu', 10))
corrplot(M, order = 'AOE', addCoef.col = 'black', tl.pos = 'd',
cl.pos = 'n', col = COL2('PiYG'))
corrplot(M, method = 'square', order = 'AOE', addCoef.col = 'black', tl.pos = 'd',
cl.pos = 'n', col = COL2('BrBG'))
## bottom color legend, diagonal text legend, rotate text label
corrplot(M, order = 'AOE', cl.pos = 'b', tl.pos = 'd',
col = COL2('PRGn'), diag = FALSE)
## text labels rotated 45 degrees and wider color legend with numbers right aligned
corrplot(M, type = 'lower', order = 'hclust', tl.col = 'black',
cl.ratio = 0.2, tl.srt = 45, col = COL2('PuOr', 10))
## remove color legend, text legend and principal diagonal glyph
corrplot(M, order = 'AOE', cl.pos = 'n', tl.pos = 'n',
col = c('white', 'black'), bg = 'gold2')
Visualize non-correlation matrix, NA value and math label
We can visualize a non-correlation matrix by set
is.corr=FALSE, and assign colors by col.lim.
If the matrix have both positive and negative values, the matrix
transformation keep every values positiveness and negativeness.
If your matrix is rectangular, you can adjust the aspect ratio with
the win.asp parameter to make the matrix rendered as a
square.
## matrix in [20, 26], grid.col
N1 = matrix(runif(80, 20, 26), 8)
corrplot(N1, is.corr = FALSE, col.lim = c(20, 30), method = 'color', tl.pos = 'n',
col = COL1('YlGn'), cl.pos = 'b', addgrid.col = 'white', addCoef.col = 'grey50')
## matrix in [-15, 10]
N2 = matrix(runif(80, -15, 10), 8)
## using sequential colors, transKeepSign = FALSE
corrplot(N2, is.corr = FALSE, transKeepSign = FALSE, method = 'color', col.lim = c(-15, 10),
tl.pos = 'n', col = COL1('YlGn'), cl.pos = 'b', addCoef.col = 'grey50')
## using diverging colors, transKeepSign = TRUE (default)
corrplot(N2, is.corr = FALSE, col.lim = c(-15, 10),
tl.pos = 'n', col = COL2('PiYG'), cl.pos = 'b', addCoef.col = 'grey50')
## using diverging colors
corrplot(N2, is.corr = FALSE, method = 'color', col.lim = c(-15, 10), tl.pos = 'n',
col = COL2('PiYG'), cl.pos = 'b', addCoef.col = 'grey50')
Notice: when is.corr is TRUE,
col.lim only affect the color legend If you change it, the
color on correlation matrix plot is still assigned on
c(-1, 1)
# when is.corr=TRUE, col.lim only affect the color legend display
corrplot(M/2)
corrplot(M/2, col.lim=c(-0.5, 0.5))
By default, corrplot renders NA values as
'?' characters. Using na.label parameter, it
is possible to use a different value (max. two characters are
supported).
Since version 0.78, it is possible to use plotmath
expression in variable names. To activate plotmath rendering, prefix
your label with '$'.
M2 = M
diag(M2) = NA
colnames(M2) = rep(c('$alpha+beta', '$alpha[0]', '$alpha[beta]'),
c(4, 4, 3))
rownames(M2) = rep(c('$Sigma[i]^n', '$sigma', '$alpha[0]^100', '$alpha[beta]'),
c(2, 4, 2, 3))
corrplot(10*abs(M2), is.corr = FALSE, col.lim = c(0, 10), tl.cex = 1.5)
Visualize p-value and confidence interval
corrplot() can also visualize p-value and confidence
interval on the correlation matrix plot. Here are some important
parameters.
About p-value:
p.mat is the p-value matrix, if NULL,
parameter sig.level, insig, pch,
pch.col, pch.cex are invalid.sig.level is significant level, with default value
0.05. If the p-value in p-mat is bigger than
sig.level, then the corresponding correlation coefficient
is regarded as insignificant. If insig is
'label_sig', sig.level can be an increasing
vector of significance levels, in which case pch will be
used once for the highest p-value interval and multiple times
(e.g. '*', '**', '***') for each
lower p-value interval.insig Character, specialized insignificant correlation
coefficients, 'pch' (default), 'p-value',
'blank', 'n', or 'label_sig'. If
'blank', wipe away the corresponding glyphs; if
'p-value', add p-values the corresponding glyphs; if
'pch', add characters (see pch for details) on
corresponding glyphs; if 'n', don’t take any measures; if
'label_sig', mark significant correlations with
pch (see sig.level).pch is for adding character on the glyphs of
insignificant correlation coefficients (only valid when insig is
'pch'). See ?par .
About confidence interval:
plotCI is character for the method of plotting
confidence interval. If 'n', don’t plot confidence
interval. If 'rect', plot rectangles whose upper side means
upper bound and lower side means lower bound respectively.lowCI.mat is the matrix of the lower bound of
confidence interval.uppCI.mat is the Matrix of the upper bound of
confidence interval.
We can get p-value matrix and confidence intervals matrix by
cor.mtest() which returns a list containing:
p is the p-values matrix.lowCI is the lower bound of confidence interval
matrix.uppCI is the lower bound of confidence interval
matrix.
testRes = cor.mtest(mtcars, conf.level = 0.95)
## specialized the insignificant value according to the significant level
corrplot(M, p.mat = testRes$p, sig.level = 0.10, order = 'hclust', addrect = 2)
## leave blank on non-significant coefficient
## add significant correlation coefficients
corrplot(M, p.mat = testRes$p, method = 'circle', type = 'lower', insig='blank',
addCoef.col ='black', number.cex = 0.8, order = 'AOE', diag=FALSE)
## leave blank on non-significant coefficient
## add all correlation coefficients
corrplot(M, p.mat = testRes$p, method = 'circle', type = 'lower', insig='blank',
order = 'AOE', diag = FALSE)$corrPos -> p1
text(p1$x, p1$y, round(p1$corr, 2))
## add p-values on no significant coefficients
corrplot(M, p.mat = testRes$p, insig = 'p-value')
## add all p-values
corrplot(M, p.mat = testRes$p, insig = 'p-value', sig.level = -1)
## add significant level stars
corrplot(M, p.mat = testRes$p, method = 'color', diag = FALSE, type = 'upper',
sig.level = c(0.001, 0.01, 0.05), pch.cex = 0.9,
insig = 'label_sig', pch.col = 'grey20', order = 'AOE')
## add significant level stars and cluster rectangles
corrplot(M, p.mat = testRes$p, tl.pos = 'd', order = 'hclust', addrect = 2,
insig = 'label_sig', sig.level = c(0.001, 0.01, 0.05),
pch.cex = 0.9, pch.col = 'grey20')
Visualize confidence interval.
# Visualize confidence interval
corrplot(M, lowCI = testRes$lowCI, uppCI = testRes$uppCI, order = 'hclust',
tl.pos = 'd', rect.col = 'navy', plotC = 'rect', cl.pos = 'n')
# Visualize confidence interval and cross the significant coefficients
corrplot(M, p.mat = testRes$p, lowCI = testRes$lowCI, uppCI = testRes$uppCI,
addrect = 3, rect.col = 'navy', plotC = 'rect', cl.pos = 'n')
References
Michael Friendly (2002). Corrgrams: Exploratory displays for
correlation matrices. The American Statistician, 56, 316–324.
D.J. Murdoch, E.D. Chow (1996). A graphical display of large
correlation matrices. The American Statistician, 50, 178–180.
Michael Hahsler, Christian Buchta and Kurt Hornik (2020).
seriation: Infrastructure for Ordering Objects Using Seriation. R
package version 1.2-9. https://CRAN.R-project.org/package=seriation
Hahsler M, Hornik K, Buchta C (2008). “Getting things in order:
An introduction to the R package seriation.” Journal of Statistical
Software, 25(3), 1-34. ISSN 1548-7660, doi:
10.18637/jss.v025.i03 (URL: https://doi.org/10.18637/jss.v025.i03), <URL: https://www.jstatsoft.org/v25/i03/>.
corrplot/inst/doc/corrplot-intro.Rmd 0000644 0001762 0000144 00000047346 14703115404 017316 0 ustar ligges users ---
title: 'An Introduction to corrplot Package'
author: 'Taiyun Wei, Viliam Simko'
date: '`r Sys.Date()`'
output:
prettydoc::html_pretty:
theme: cayman
toc: true
toc-title: 'Table of Contents'
vignette: >
%\VignetteIndexEntry{An Introduction to corrplot Package}
%\VignetteEncoding{UTF-8}
%\VignetteEngine{knitr::rmarkdown}
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(
fig.align = 'center',
fig.path = 'webimg/',
fig.width = 7,
fig.height = 7,
out.width = '600px',
dev = 'png')
get_os = function() {
sysinf = Sys.info()
if (!is.null(sysinf)) {
os = sysinf['sysname']
if (os == 'Darwin')
os = 'osx'
} else { ## mystery machine
os = .Platform$OS.type
if (grepl('^darwin', R.version$os))
os = 'osx'
if (grepl('linux-gnu', R.version$os))
os = 'linux'
}
tolower(os)
}
if(get_os() =='windows' & capabilities('cairo') | all(capabilities(c('cairo', 'X11')))) {
knitr::opts_chunk$set(dev.args = list(type='cairo'))
}
```
## Introduction
R package **corrplot** provides a visual exploratory tool on correlation matrix that
supports automatic variable reordering to help detect hidden patterns among variables.
corrplot is very easy to use and provides a rich array of plotting options in
visualization method, graphic layout, color, legend, text labels, etc.
It also provides p-values and confidence intervals to help users determine the
statistical significance of the correlations.
`corrplot()` has about 50 parameters, however the mostly common ones are only a few.
We can get a correlation matrix plot with only one line of code in most scenes.
The mostly using parameters include `method`, `type`, `order`, `diag`, and etc.
There are seven visualization methods (parameter `method`) in
corrplot package, named `'circle'`, `'square'`, `'ellipse'`,
`'number'`, `'shade'`, `'color'`, `'pie'`. Color intensity of the glyph
is proportional to the correlation coefficients by default color setting.
- `'circle'` and `'square'`, the **areas** of circles or squares show the
absolute value of corresponding correlation coefficients.
- `'ellipse'`, the ellipses have their eccentricity parametrically scaled to the correlation value.
It comes from D.J. Murdoch and E.D. Chow's job, see in section References.
- `'number'`, coefficients numbers with different color.
- `'color'`, square of equal size with different color.
- `'shade'`, similar to `'color'`, but the negative coefficients glyphs are shaded.
Method `'pie'` and `'shade'` come from Michael Friendly's job.
- `'pie'`, the circles are filled clockwise for positive values, anti-clockwise for negative
values.
`corrplot.mixed()` is a wrapped function for mixed visualization style,
which can set the visual methods of lower and upper triangular
separately.
There are three layout types (parameter `type`): `'full'`, `'upper'` and
`'lower'`.
The correlation matrix can be reordered according to the correlation
matrix coefficients. This is important to identify the hidden structure
and pattern in the matrix.
```{r intro}
library(corrplot)
M = cor(mtcars)
corrplot(M, method = 'number') # colorful number
corrplot(M, method = 'color', order = 'alphabet')
corrplot(M) # by default, method = 'circle'
corrplot(M, order = 'AOE') # after 'AOE' reorder
corrplot(M, method = 'shade', order = 'AOE', diag = FALSE)
corrplot(M, method = 'square', order = 'FPC', type = 'lower', diag = FALSE)
corrplot(M, method = 'ellipse', order = 'AOE', type = 'upper')
corrplot.mixed(M, order = 'AOE')
corrplot.mixed(M, lower = 'shade', upper = 'pie', order = 'hclust')
```
## Reorder a correlation matrix
The details of four `order` algorithms, named `'AOE'`, `'FPC'`,
`'hclust'`, `'alphabet'` are as following.
- `'AOE'` is for the angular order of the eigenvectors. It is
calculated from the order of the angles $a_i$,
$$
a_i =
\begin{cases}
\arctan (e_{i2}/e_{i1}), & \text{if $e_{i1}>0$;}
\newline
\arctan (e_{i2}/e_{i1}) + \pi, & \text{otherwise.}
\end{cases}
$$
where $e_1$ and $e_2$ are the largest two eigenvalues of the
correlation matrix. See [Michael Friendly
(2002)](http://www.datavis.ca/papers/corrgram.pdf) for details.
- `'FPC'` for the first principal component order.
- `'hclust'` for hierarchical clustering order, and `'hclust.method'`
for the agglomeration method to be used. `'hclust.method'` should be
one of `'ward'`, `'ward.D'`, `'ward.D2'`, `'single'`, `'complete'`,
`'average'`, `'mcquitty'`, `'median'` or `'centroid'`.
- `'alphabet'` for alphabetical order.
You can also reorder the matrix 'manually' via function
`corrMatOrder()`.
If using `'hclust'`, `corrplot()` can draw rectangles around the plot of
correlation matrix based on the results of hierarchical clustering.
```{r hclust}
corrplot(M, order = 'hclust', addrect = 2)
corrplot(M, method = 'square', diag = FALSE, order = 'hclust',
addrect = 3, rect.col = 'blue', rect.lwd = 3, tl.pos = 'd')
```
R package **seriation** provides the infrastructure for ordering objects with an
implementation of several seriation/sequencing/ordination techniques to reorder
matrices, dissimilarity matrices, and dendrograms. For more information,
see in section References.
We can reorder the matrix via **seriation** package and then corrplot it.
Here are some examples.
```{r seriation}
library(seriation)
list_seriation_methods('matrix')
list_seriation_methods('dist')
data(Zoo)
Z = cor(Zoo[, -c(15, 17)])
dist2order = function(corr, method, ...) {
d_corr = as.dist(1 - corr)
s = seriate(d_corr, method = method, ...)
i = get_order(s)
return(i)
}
```
Methods `'PCA_angle'` and `'HC'` in **seriation**, are same as `'AOE'` and `'hclust'`
separately in `corrplot()` and `corrMatOrder()`.
Here are some plots after seriation.
```{r seriation-plot}
# Fast Optimal Leaf Ordering for Hierarchical Clustering
i = dist2order(Z, 'OLO')
corrplot(Z[i, i], cl.pos = 'n')
# Quadratic Assignment Problem
i = dist2order(Z, 'QAP_2SUM')
corrplot(Z[i, i], cl.pos = 'n')
# Multidimensional Scaling
i = dist2order(Z, 'MDS_nonmetric')
corrplot(Z[i, i], cl.pos = 'n')
# Simulated annealing
i = dist2order(Z, 'ARSA')
corrplot(Z[i, i], cl.pos = 'n')
# TSP solver
i = dist2order(Z, 'TSP')
corrplot(Z[i, i], cl.pos = 'n')
# Spectral seriation
i = dist2order(Z, 'Spectral')
corrplot(Z[i, i], cl.pos = 'n')
```
`corrRect()` can add rectangles on the plot with three ways(parameter
`index`, `name` and `namesMat`) after `corrplot()`.
We can use pipe operator `*>%` in package `magrittr` with more convenience.
Since R 4.1.0, `|>` is supported without extra package.
```{r rectangles}
library(magrittr)
# Rank-two ellipse seriation, use index parameter
i = dist2order(Z, 'R2E')
corrplot(Z[i, i], cl.pos = 'n') %>% corrRect(c(1, 9, 15))
# use name parameter
# Since R 4.1.0, the following one line code works:
# corrplot(M, order = 'AOE') |> corrRect(name = c('gear', 'wt', 'carb'))
corrplot(Z, order = 'AOE') %>%
corrRect(name = c('tail', 'airborne', 'venomous', 'predator'))
# use namesMat parameter
r = rbind(c('eggs', 'catsize', 'airborne', 'milk'),
c('catsize', 'eggs', 'milk', 'airborne'))
corrplot(Z, order = 'hclust') %>% corrRect(namesMat = r)
```
## Change color spectra, color-legend and text-legend
We can get sequential and diverging colors from `COL1()` and `COL2()`.
The color palettes are borrowed from `RColorBrewer` package.
**Notice**: the middle color getting from `COL2()` is fixed to `'#FFFFFF'`(white),
thus we can visualizing element 0 with white color.
- `COL1()`: Get sequential colors, suitable for visualize a non-negative or
non-positive matrix (e.g. matrix in [0, 20], or [-100, -10], or [100, 500]).
- `COL2()`: Get diverging colors, suitable for visualize a matrix which elements
are partly positive and partly negative (e.g. correlation matrix in [-1, 1], or [-20, 100]).
The colors of the correlation plots can be customized by `col` in `corrplot()`.
They are distributed uniformly in `col.lim` interval.
- `col`: vector, the colors of glyphs. They are distributed uniformly in `col.lim` interval. By default,
- If `is.corr` is `TRUE`, `col` will be `COL2('RdBu', 200)`.
- If `is.corr` is `FALSE`,
- and `corr` is a non-negative or non-positive matrix, `col` will be `COL1('YlOrBr', 200)`;
- otherwise (elements are partly positive and partly negative), `col` will be `COL2('RdBu', 200)`.
- `col.lim`: the limits (x1, x2) interval for assigning color by `col`. By default,
- `col.lim` will be `c(-1, 1)` when `is.corr` is `TRUE`,
- `col.lim` will be `c(min(corr), max(corr))` when `is.corr` is `FALSE`.
- **NOTICE**: if you set `col.lim` when `is.corr` is `TRUE`, the assigning colors are still
distributed uniformly in [-1, 1], it only affect the display on color-legend.
- `is.corr`: logical, whether the input matrix is a correlation matrix or not. The default value is `TRUE`.
We can visualize a non-correlation matrix by setting `is.corr = FALSE`.
Here all diverging colors from `COL2()` and sequential colors from `COL1()` are shown below.
**Diverging colors**:
```{r echo=FALSE, fig.width = 8, fig.height = 6, out.width = '700px'}
## diverging colors
plot.new()
par(mar = c(0, 0, 0, 0) + 0.1)
plot.window(xlim = c(-0.2, 1.1), ylim = c(0, 1), xaxs = 'i', yaxs = 'i')
col = c('RdBu', 'BrBG', 'PiYG', 'PRGn', 'PuOr', 'RdYlBu')
for(i in 1:length(col)) {
colorlegend(COL2(col[i]), -10:10/10, align = 'l', cex = 0.8, xlim = c(0, 1),
ylim = c(i/length(col)-0.1, i/length(col)), vertical = FALSE)
text(-0.01, i/length(col)-0.02, col[i], adj = 0.5, pos = 2, cex = 0.8)
}
```
**Sequential colors**:
```{r echo=FALSE, fig.width = 8, fig.height = 6, out.width = '700px'}
## sequential colors
plot.new()
par(mar = c(0, 0, 0, 0) + 0.1)
plot.window(xlim = c(-0.2, 1.1), ylim = c(0, 1), xaxs = 'i', yaxs = 'i')
col = c('Oranges', 'Purples', 'Reds', 'Blues', 'Greens', 'Greys', 'OrRd',
'YlOrRd', 'YlOrBr', 'YlGn')
for(i in 1:length(col)) {
colorlegend(COL1(col[i]), 0:10, align = 'l', cex = 0.8, xlim = c(0, 1),
ylim = c(i/length(col)-0.1, i/length(col)), vertical = FALSE)
text(-0.01, i/length(col)-0.02, col[i], adj = 0.5, pos = 2)
}
```
Usage of `COL1()` and `COL2()`:
```{r eval=FALSE}
COL1(sequential = c("Oranges", "Purples", "Reds", "Blues", "Greens",
"Greys", "OrRd", "YlOrRd", "YlOrBr", "YlGn"), n = 200)
COL2(diverging = c("RdBu", "BrBG", "PiYG", "PRGn", "PuOr", "RdYlBu"), n = 200)
```
In addition, function `colorRampPalette()` is very convenient for generating color spectrum.
Parameters group `cl.*` is for color-legend. The common-using are:
- `cl.pos` is for the position of color labels. It is character or
logical. If character, it must be one of `'r'` (means right, default
if `type='upper'` or `'full'`), `'b'` (means bottom, default if
`type='lower'`) or `'n'`(means don't draw color-label).
- `cl.ratio` is to justify the width of color-legend, 0.1\~0.2 is
suggested.
Parameters group `tl.*` is for text-legend. The common-using are:
- `tl.pos` is for the position of text labels. It is character or
logical. If character, it must be one of `'lt'`, `'ld'`, `'td'`,
`'d'`, `'l'` or `'n'`. `'lt'`(default if `type='full'`) means left and top,
`'ld'`(default if `type='lower'`) means left and diagonal,
`'td'`(default if `type='upper'`) means top and diagonal(near),
`'d'` means diagonal, `'l'` means left, `'n'` means don't add text-label.
- `tl.cex` is for the size of text label (variable names).
- `tl.srt` is for text label string rotation in degrees.
```{r color}
corrplot(M, order = 'AOE', col = COL2('RdBu', 10))
corrplot(M, order = 'AOE', addCoef.col = 'black', tl.pos = 'd',
cl.pos = 'n', col = COL2('PiYG'))
corrplot(M, method = 'square', order = 'AOE', addCoef.col = 'black', tl.pos = 'd',
cl.pos = 'n', col = COL2('BrBG'))
## bottom color legend, diagonal text legend, rotate text label
corrplot(M, order = 'AOE', cl.pos = 'b', tl.pos = 'd',
col = COL2('PRGn'), diag = FALSE)
## text labels rotated 45 degrees and wider color legend with numbers right aligned
corrplot(M, type = 'lower', order = 'hclust', tl.col = 'black',
cl.ratio = 0.2, tl.srt = 45, col = COL2('PuOr', 10))
## remove color legend, text legend and principal diagonal glyph
corrplot(M, order = 'AOE', cl.pos = 'n', tl.pos = 'n',
col = c('white', 'black'), bg = 'gold2')
```
## Visualize non-correlation matrix, NA value and math label
We can visualize a non-correlation matrix by set `is.corr=FALSE`, and
assign colors by `col.lim`. If the matrix have both positive and
negative values, the matrix transformation keep every values
positiveness and negativeness.
If your matrix is rectangular, you can adjust the aspect ratio with the
`win.asp` parameter to make the matrix rendered as a square.
```{r non-corr}
## matrix in [20, 26], grid.col
N1 = matrix(runif(80, 20, 26), 8)
corrplot(N1, is.corr = FALSE, col.lim = c(20, 30), method = 'color', tl.pos = 'n',
col = COL1('YlGn'), cl.pos = 'b', addgrid.col = 'white', addCoef.col = 'grey50')
## matrix in [-15, 10]
N2 = matrix(runif(80, -15, 10), 8)
## using sequential colors, transKeepSign = FALSE
corrplot(N2, is.corr = FALSE, transKeepSign = FALSE, method = 'color', col.lim = c(-15, 10),
tl.pos = 'n', col = COL1('YlGn'), cl.pos = 'b', addCoef.col = 'grey50')
## using diverging colors, transKeepSign = TRUE (default)
corrplot(N2, is.corr = FALSE, col.lim = c(-15, 10),
tl.pos = 'n', col = COL2('PiYG'), cl.pos = 'b', addCoef.col = 'grey50')
## using diverging colors
corrplot(N2, is.corr = FALSE, method = 'color', col.lim = c(-15, 10), tl.pos = 'n',
col = COL2('PiYG'), cl.pos = 'b', addCoef.col = 'grey50')
```
Notice: when `is.corr` is `TRUE`, `col.lim` only affect the color legend If
you change it, the color on correlation matrix plot is still assigned on
`c(-1, 1)`
```{r col-lim}
# when is.corr=TRUE, col.lim only affect the color legend display
corrplot(M/2)
corrplot(M/2, col.lim=c(-0.5, 0.5))
```
By default, **corrplot** renders NA values as `'?'` characters. Using
`na.label` parameter, it is possible to use a different value (max. two
characters are supported).
Since version `0.78`, it is possible to use
[plotmath](https://www.rdocumentation.org/packages/grDevices/topics/plotmath)
expression in variable names. To activate plotmath rendering, prefix
your label with `'$'`.
```{r NA-math}
M2 = M
diag(M2) = NA
colnames(M2) = rep(c('$alpha+beta', '$alpha[0]', '$alpha[beta]'),
c(4, 4, 3))
rownames(M2) = rep(c('$Sigma[i]^n', '$sigma', '$alpha[0]^100', '$alpha[beta]'),
c(2, 4, 2, 3))
corrplot(10*abs(M2), is.corr = FALSE, col.lim = c(0, 10), tl.cex = 1.5)
```
## Visualize p-value and confidence interval
`corrplot()` can also visualize p-value and confidence interval on the
correlation matrix plot. Here are some important parameters.
About p-value:
- `p.mat` is the p-value matrix, if `NULL`, parameter `sig.level`,
`insig, pch`, `pch.col`, `pch.cex` are invalid.
- `sig.level` is significant level, with default value 0.05. If the
p-value in `p-mat` is bigger than `sig.level`, then the
corresponding correlation coefficient is regarded as insignificant.
If `insig` is `'label_sig'`, `sig.level` can be an increasing vector
of significance levels, in which case `pch` will be used once for
the highest p-value interval and multiple times (e.g. `'*'`, `'**'`,
`'***'`) for each lower p-value interval.
- `insig` Character, specialized insignificant correlation
coefficients, `'pch'` (default), `'p-value'`, `'blank',` `'n'`, or
`'label_sig'`. If `'blank'`, wipe away the corresponding glyphs; if
`'p-value'`, add p-values the corresponding glyphs; if `'pch'`, add
characters (see pch for details) on corresponding glyphs; if `'n'`,
don't take any measures; if `'label_sig'`, mark significant
correlations with `pch` (see `sig.level`).
- `pch` is for adding character on the glyphs of insignificant
correlation coefficients (only valid when insig is `'pch'`). See
`?par` .
About confidence interval:
- `plotCI` is character for the method of plotting confidence
interval. If `'n'`, don't plot confidence interval. If `'rect'`,
plot rectangles whose upper side means upper bound and lower side
means lower bound respectively.
- `lowCI.mat` is the matrix of the lower bound of confidence interval.
- `uppCI.mat` is the Matrix of the upper bound of confidence interval.
We can get p-value matrix and confidence intervals matrix by
`cor.mtest()` which returns a list containing:
- `p` is the p-values matrix.
- `lowCI` is the lower bound of confidence interval matrix.
- `uppCI` is the lower bound of confidence interval matrix.
```{r test}
testRes = cor.mtest(mtcars, conf.level = 0.95)
## specialized the insignificant value according to the significant level
corrplot(M, p.mat = testRes$p, sig.level = 0.10, order = 'hclust', addrect = 2)
## leave blank on non-significant coefficient
## add significant correlation coefficients
corrplot(M, p.mat = testRes$p, method = 'circle', type = 'lower', insig='blank',
addCoef.col ='black', number.cex = 0.8, order = 'AOE', diag=FALSE)
```
```{r special}
## leave blank on non-significant coefficient
## add all correlation coefficients
corrplot(M, p.mat = testRes$p, method = 'circle', type = 'lower', insig='blank',
order = 'AOE', diag = FALSE)$corrPos -> p1
text(p1$x, p1$y, round(p1$corr, 2))
```
```{r p-values}
## add p-values on no significant coefficients
corrplot(M, p.mat = testRes$p, insig = 'p-value')
## add all p-values
corrplot(M, p.mat = testRes$p, insig = 'p-value', sig.level = -1)
## add significant level stars
corrplot(M, p.mat = testRes$p, method = 'color', diag = FALSE, type = 'upper',
sig.level = c(0.001, 0.01, 0.05), pch.cex = 0.9,
insig = 'label_sig', pch.col = 'grey20', order = 'AOE')
## add significant level stars and cluster rectangles
corrplot(M, p.mat = testRes$p, tl.pos = 'd', order = 'hclust', addrect = 2,
insig = 'label_sig', sig.level = c(0.001, 0.01, 0.05),
pch.cex = 0.9, pch.col = 'grey20')
```
Visualize confidence interval.
```{r confidence-interval}
# Visualize confidence interval
corrplot(M, lowCI = testRes$lowCI, uppCI = testRes$uppCI, order = 'hclust',
tl.pos = 'd', rect.col = 'navy', plotC = 'rect', cl.pos = 'n')
# Visualize confidence interval and cross the significant coefficients
corrplot(M, p.mat = testRes$p, lowCI = testRes$lowCI, uppCI = testRes$uppCI,
addrect = 3, rect.col = 'navy', plotC = 'rect', cl.pos = 'n')
```
## References
- Michael Friendly (2002). Corrgrams: Exploratory displays for correlation
matrices. The American Statistician, 56, 316--324.
- D.J. Murdoch, E.D. Chow (1996). A graphical display of large correlation
matrices. The American Statistician, 50, 178--180.
- Michael Hahsler, Christian Buchta and Kurt Hornik (2020). seriation: Infrastructure for Ordering
Objects Using Seriation. R package version 1.2-9. https://CRAN.R-project.org/package=seriation
- Hahsler M, Hornik K, Buchta C (2008). "Getting things in order: An introduction to the R package
seriation." _Journal of Statistical Software_, *25*(3), 1-34. ISSN 1548-7660, doi:
10.18637/jss.v025.i03 (URL: https://doi.org/10.18637/jss.v025.i03),