An Introduction to corrplot Package

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.

library(corrplot)

## corrplot 0.92 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] "BEA"       "BEA_TSP"   "Heatmap"   "Identity"  "PCA"       "PCA_angle"
## [7] "Random"    "Reverse"

list_seriation_methods('dist')

##  [1] "ARSA"          "BBURCG"        "BBWRCG"        "GW"           
##  [5] "GW_average"    "GW_complete"   "GW_single"     "GW_ward"      
##  [9] "HC"            "HC_average"    "HC_complete"   "HC_single"    
## [13] "HC_ward"       "Identity"      "MDS"           "MDS_angle"    
## [17] "MDS_metric"    "MDS_nonmetric" "OLO"           "OLO_average"  
## [21] "OLO_complete"  "OLO_single"    "OLO_ward"      "QAP_2SUM"     
## [25] "QAP_BAR"       "QAP_Inertia"   "QAP_LS"        "R2E"          
## [29] "Random"        "SA"            "SPIN_NH"       "SPIN_STS"     
## [33] "Spectral"      "Spectral_norm" "TSP"           "VAT"

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')
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)
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/>.