11/23/2018 Visualize correlation matrix using correlogram - Easy Guides - Wiki - STHDA

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Visualize correlation matrix using correlogram

 Visualize correlation matrix using correlogram

Tools

Introduction
Install R corrplot package
Data for correlation analysis
Computing correlation matrix
Correlogram : Visualizing the correlation matrix
Visualization methods
Types of correlogram layout
Reordering the correlation matrix
Changing the color of the correlogram
Changing the color and the rotation of text labels
Combining correlogram with the signi cance test
Computing the p-value of correlations
Add signi cance level to the correlogram

Customize the correlogram

Conclusions
Infos

Introduction
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This article describes how to plot a correlogram in R. Correlogram is a graph of correlation matrix. It is very
useful to highlight the most correlated variables in a data table. In this plot, correlation coe cients is colored
according to the value. Correlation matrix can be also reordered according to the degree of association between
variables. The R corrplot package is used here.

 Note that online software is also available here to compute correlation matrix and to plot a

correlogram without any installation.

Install R corrplot package

corrplot package is required to execute the R code in this article.

install.packages("corrplot")

Data for correlation analysis

The mtcars data is used to compute correlation matrix.

head(mtcars)

mpg cyl disp hp drat wt qsec vs am gear carb

Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1

Computing correlation matrix

M<-cor(mtcars)
head(round(M,2))

mpg cyl disp hp drat wt qsec vs am gear carb

mpg 1.00 -0.85 -0.85 -0.78 0.68 -0.87 0.42 0.66 0.60 0.48 -0.55
cyl -0.85 1.00 0.90 0.83 -0.70 0.78 -0.59 -0.81 -0.52 -0.49 0.53
disp -0.85 0.90 1.00 0.79 -0.71 0.89 -0.43 -0.71 -0.59 -0.56 0.39
hp -0.78 0.83 0.79 1.00 -0.45 0.66 -0.71 -0.72 -0.24 -0.13 0.75
drat 0.68 -0.70 -0.71 -0.45 1.00 -0.71 0.09 0.44 0.71 0.70 -0.09
wt -0.87 0.78 0.89 0.66 -0.71 1.00 -0.17 -0.55 -0.69 -0.58 0.43

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Correlogram : Visualizing the correlation matrix

R corrplot function is used to plot the graph of the correlation matrix.

The simpli ed format of the function is :

corrplot(corr, method="circle")

Arguments Description

corr The correlation matrix to visualize. To visualize a general matrix, please use is.corr=FALSE.

method The visualization method : “circle”, “color”, “number”, etc.

Visualization methods
Seven di erent visualization methods can be used : “circle”, “square”, “ellipse”, “number”, “shade”, “color”, “pie”.

library(corrplot)
corrplot(M, method="circle")

corrplot(M, method="pie")

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corrplot(M, method="color")

 Positive correlations are displayed in blue and negative correlations in red color. Color intensity and the
size of the circle are proportional to the correlation coe cients.

Display the correlation coe cient :

corrplot(M, method="number")

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Types of correlogram layout

There are three types of layout :

“full” (default) : display full correlation matrix

“upper”: display upper triangular of the correlation matrix
“lower”: display lower triangular of the correlation matrix

corrplot(M, type="upper")

corrplot(M, type="lower")

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Reordering the correlation matrix

The correlation matrix can be reordered according to the correlation coe cient. This is important to identify
the hidden structure and pattern in the matrix. “hclust” for hierarchical clustering order is used in the following
examples.

# correlogram with hclust reordering

corrplot(M, type="upper", order="hclust")

# Using different color spectrum

col<- colorRampPalette(c("red", "white", "blue"))(20)
corrplot(M, type="upper", order="hclust", col=col)

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# Change background color to lightblue

corrplot(M, type="upper", order="hclust", col=c("black", "white"),
bg="lightblue")

Changing the color of the correlogram

As shown in the above section, the color of the correlogram can be customized. RcolorBrewer palette of colors are
used in the R script below :

library(RColorBrewer)
corrplot(M, type="upper", order="hclust",
col=brewer.pal(n=8, name="RdBu"))

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corrplot(M, type="upper", order="hclust",

col=brewer.pal(n=8, name="RdYlBu"))

corrplot(M, type="upper", order="hclust",

col=brewer.pal(n=8, name="PuOr"))

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Changing the color and the rotation of text labels

tl.col (for text label color) and tl.srt (for text label string rotation) are used to change text colors and rotations.

corrplot(M, type="upper", order="hclust", tl.col="black", tl.srt=45)

Combining correlogram with the signi cance test

Computing the p-value of correlations

To compute the matrix of p-value, a custom R function is used :

# mat : is a matrix of data

# ... : further arguments to pass to the native R cor.test function
cor.mtest <- function(mat, ...) {
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mat <- as.matrix(mat)

n <- ncol(mat)
p.mat<- matrix(NA, n, n)
diag(p.mat) <- 0
for (i in 1:(n - 1)) {
for (j in (i + 1):n) {
tmp <- cor.test(mat[, i], mat[, j], ...)
p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
}
}
colnames(p.mat) <- rownames(p.mat) <- colnames(mat)
p.mat
}
# matrix of the p-value of the correlation
p.mat <- cor.mtest(mtcars)
head(p.mat[, 1:5])

mpg cyl disp hp drat

mpg 0.000e+00 6.113e-10 9.380e-10 1.788e-07 1.776e-05
cyl 6.113e-10 0.000e+00 1.803e-12 3.478e-09 8.245e-06
disp 9.380e-10 1.803e-12 0.000e+00 7.143e-08 5.282e-06
hp 1.788e-07 3.478e-09 7.143e-08 0.000e+00 9.989e-03
drat 1.776e-05 8.245e-06 5.282e-06 9.989e-03 0.000e+00
wt 1.294e-10 1.218e-07 1.222e-11 4.146e-05 4.784e-06

Add signi cance level to the correlogram

# Specialized the insignificant value according to the significant level

corrplot(M, type="upper", order="hclust",
p.mat = p.mat, sig.level = 0.01)

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# Leave blank on no significant coefficient

corrplot(M, type="upper", order="hclust",
p.mat = p.mat, sig.level = 0.01, insig = "blank")

In the above gure, correlations with p-value > 0.01 are considered as insigni cant. In this case the correlation
coe cient values are leaved blank or crosses are added.

Customize the correlogram

col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))

corrplot(M, method="color", col=col(200),
type="upper", order="hclust",
addCoef.col = "black", # Add coefficient of correlation
tl.col="black", tl.srt=45, #Text label color and rotation
# Combine with significance
p.mat = p.mat, sig.level = 0.01, insig = "blank",
# hide correlation coefficient on the principal diagonal
diag=FALSE
)

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Conclusions

Use corrplot() R function to plot an elegant graph of a correlation matrix.

Infos
References: corrplot intro

 This analysis was performed using R (ver. 3.1.0).

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