Correlogram

Authors

[Editor] Yinying Chai;

[Contributors] ShiXiang Wang, Peng Luo, Hong Yang, KeXin Li, Ying Shi, Hu Zheng.

Correlogram or Correlation diagrams are often used to summarize the correlation information of various groups of data in the entire dataset.

Example

Correlogram DEMO

For example, the above diagram is a correlation heatmap of various groups of data in the mtcars dataset. Colors are used to represent the pairwise correlations of data in different groups, and the shade of the color represents the magnitude of the P-value.

Setup

  • System Requirements: Cross-platform (Linux/MacOS/Windows)

  • Programming Language: R

  • Dependencies: GGally; corrplot; ggcorrplot; corrgram

# Install packages
if (!requireNamespace("GGally", quietly = TRUE)) {
  install.packages("GGally")
}
if (!requireNamespace("corrplot", quietly = TRUE)) {
  install.packages("corrplot")
}
if (!requireNamespace("ggcorrplot", quietly = TRUE)) {
  install.packages("ggcorrplot")
}
if (!requireNamespace("corrgram", quietly = TRUE)) {
  install.packages("corrgram")
}

# Load packages
library(GGally)
library(corrplot)
library(ggcorrplot)
library(corrgram)

Data Preparation

The correlation heatmap is mainly drawn using the built-in datasets in R.

data("flea", package = "GGally")
data_flea <- flea

data("mtcars", package = "datasets")
data_mtcars <- mtcars

data("tips", package = "GGally")
data_tips <- tips

Visualization

1. GGally Package

GGally is a commonly used tool for drawing correlation diagrams. It allows the injection of ggplot2 code but does not have a sorting function.

Drawing of Basic Correlation Diagram

ggpairs(data_flea, columns = 2:5)

The above diagram shows the correlation visualization of each group of data in the flea dataset. The picture consists of three parts: the scatter plot of the correlation between the corresponding two groups of data in the lower part; the density plot of a single group of data on the diagonal; and the Pearson correlation coefficient values of the corresponding two groups of data in the upper part.

Introducing ggplot2 Codes to Color Each Category

ggpairs(data_flea, columns = 2:4, ggplot2::aes(colour=species,alpha=0.7))

The above diagram, on the basis of correlation visualization, classifies each category by color.

Customizing the Plotting Type

ggpairs(data_tips[, c(1, 3, 4, 2)])

summary(data_tips)
   total_bill         tip             sex      smoker      day         time    
 Min.   : 3.07   Min.   : 1.000   Female: 87   No :151   Fri :19   Dinner:176  
 1st Qu.:13.35   1st Qu.: 2.000   Male  :157   Yes: 93   Sat :87   Lunch : 68  
 Median :17.80   Median : 2.900                          Sun :76               
 Mean   :19.79   Mean   : 2.998                          Thur:62               
 3rd Qu.:24.13   3rd Qu.: 3.562                                                
 Max.   :50.81   Max.   :10.000                                                
      size     
 Min.   :1.00  
 1st Qu.:2.00  
 Median :2.00  
 Mean   :2.57  
 3rd Qu.:3.00  
 Max.   :6.00

In the above diagram, tatal_bill and tip are quantitative data, while sex and smoker are qualitative data. In the lower part, scatter plots, histograms, and bar charts of pairwise correlations are mainly drawn according to different data types; in the diagonal part, the distribution diagrams of each group of data are shown; in the upper part, pairwise correlation line charts are drawn according to different data types, and for two quantitative data, the Pearson correlation coefficient values are given.

# Changing the plotting type
ggpairs(
  data_tips[, c(1, 3, 4, 2)],
  upper = list(continuous = "density",
               combo = "box_no_facet"),
  lower = list(continuous = "points",
               combo = "dot_no_facet")
)

Through customization, the histogram in the lower part is modified into a scatter plot, and the correlation coefficient values in the upper part are modified into a density plot.

Correlation Visualization

Visualize the correlation coefficients.

ggcorr(data_mtcars) # Draw a correlation coefficient heatmap, with Pearson as the default

The above diagram visualizes the correlation coefficients through the ggcorr๏ผˆ๏ผ‰ function.

The method parameter of ggcorr:

The default is in the form of c("pairwise", "pearson"). The first parameter is to determine the handling of missing values when calculating the covariance, and the second parameter is used to determine the type of correlation coefficient, such as "pearson", "kendall" or "spearman".

2. corrplot Package

The corrplot package is a commonly used tool for correlation visualization, which has powerful customization functions and a sorting function.

Basic Plotting

corr <- cor(data_mtcars)
corrplot(corr)

Parameter Customization

The main key parameters of corrplot():

corr The correlation coefficient matrix to be visualized

method The shape of the visualization

type The display range (full, lower, upper)

col The color of the graph display

addCoef.col The color of the correlation coefficient values

order The sorting method of the correlation coefficients

is.corr Whether to draw a correlation coefficient plot, which is TRUE by default. It can also achieve the visualization of non-correlation coefficients. Just set this parameter to FALSE.

โ€ฆโ€ฆ

corrplot(corr,method = "ellipse" ,#method, specify the visualization shape
         order = "AOE", #order, the sorting method of the correlation coefficients
         addCoef.col="black", # Specify the color of the correlation coefficients
         type="lower") # Specify the display part

The above diagram is a correlation coefficient heatmap of the mtcars dataset.

  • type="lower" specifies to display the lower part of the heatmap.

  • The shade of the color represents the magnitude of the correlation coefficient.

  • The shape of the ellipse represents the correlation coefficient: the greater the eccentricity, the flatter the ellipse, and the larger the absolute value of the correlation coefficient; the smaller the eccentricity, the rounder the ellipse, and the smaller the absolute value of the correlation coefficient. The direction of the long axis of the ellipse represents the positive or negative of the correlation coefficient. The upper right - lower left direction corresponds to a positive value, and the upper left - lower right direction corresponds to a negative value.

Adding Significance Labels

res1 <-cor.mtest(data_mtcars, conf.level= .95)
corrplot(corr, method= "circle",
         p.mat= res1$p, sig.level= 0.01, # P-values greater than 0.01 are considered to have no statistical significance
         mar= c(1,1,1,1))

The above diagram adds significance labels on the basis of the correlation coefficient heatmap. P-values greater than 0.01 are regarded as having no statistical significance.

3. ggcorrplot Package

The ggcorrplot package is equivalent to a simplified version of the corrplot package, mainly including the calculation function of cor_pmat and the plotting function of ggcorrplot.

Calculating P-values with cor_pmat

p.mat <- cor_pmat(data_mtcars)
head(p.mat[, 1:6])
              mpg          cyl         disp           hp         drat
mpg  0.000000e+00 6.112687e-10 9.380327e-10 1.787835e-07 1.776240e-05
cyl  6.112687e-10 0.000000e+00 1.802838e-12 3.477861e-09 8.244636e-06
disp 9.380327e-10 1.802838e-12 0.000000e+00 7.142679e-08 5.282022e-06
hp   1.787835e-07 3.477861e-09 7.142679e-08 0.000000e+00 9.988772e-03
drat 1.776240e-05 8.244636e-06 5.282022e-06 9.988772e-03 0.000000e+00
wt   1.293959e-10 1.217567e-07 1.222320e-11 4.145827e-05 4.784260e-06
               wt
mpg  1.293959e-10
cyl  1.217567e-07
disp 1.222320e-11
hp   4.145827e-05
drat 4.784260e-06
wt   0.000000e+00

Plotting with ggcorrplot

ggcorrplot(corr, method = "square" )
Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
โ„น Please use tidy evaluation idioms with `aes()`.
โ„น See also `vignette("ggplot2-in-packages")` for more information.
โ„น The deprecated feature was likely used in the ggcorrplot package.
  Please report the issue at <https://github.com/kassambara/ggcorrplot/issues>.

The above diagram is a color heatmap of the correlation coefficients of the mtcar dataset.

ggcorrplot(corr, method = "circle" )

Here we have changed the plotting type to a circle.

4. corrgram Package

The corrgram package is also a good choice for drawing correlation diagrams. It can select the content to be displayed in the upper, lower, and diagonal parts.

We mainly use the corrgram() function to draw the correlation diagram:

  • cor.method determines the type of correlation coefficient, pearson (default), spearman, kendall

Different methods can be used for visualization:

  • panel.ellipse displays an ellipse
  • panel.shade is used for color blocks
  • panel.pie is used for pie charts
  • panel.pts is used for scatter plots
corrgram(data_mtcars, order=TRUE, 
         lower.panel=panel.shade, # Color blocks
         upper.panel=panel.pie, # Pie chart
         text.panel=panel.txt, 
         main="Car Milage Data in PC2/PC1 Order")

By setting lower.panel=panel.shade and upper.panel=panel.pie, the upper part is set as a pie chart, and the lower part is set as a color diagram.

corrgram(data_mtcars, order=TRUE, 
         lower.panel=panel.ellipse, # Display an ellipse
         upper.panel=panel.pts,  # Scatter plot
         text.panel=panel.txt, 
         diag.panel=panel.minmax, 
         main="Car Milage Data in PC2/PC1 Order")

By setting lower.panel=panel.ellipse and upper.panel=panel.pts, the upper part is set as a scatter plot, and the lower part is set as an ellipse diagram (where the red line is the fitted curve).

corrgram(data_mtcars, order=NULL, 
         lower.panel=panel.shade, # Color blocks
         upper.panel=NULL, 
         text.panel=panel.txt, 
         main="Car Milage Data (unsorted)")

By setting lower.panel=panel.shade and upper.panel=NULL, only the color diagram in the lower part is displayed.

Applications

CorrelogramApp1
Figureย 1: Applications of Correlogram

The above diagram is a correlation diagram based on the ANI values of strains. The ANI values between each indicator strain are calculated using the JSpecies software and used for the construction of the Pearson correlation matrix. This diagram shows the correlations constructed and sorted by hierarchical clustering using the corrplot package. [1]

CorrelogramApp2
Figureย 2: Applications of Correlogram

The above diagram shows the correlations between Gain [FF], ILP, wpm, RR, R r-words, R p-words, RN, and VA. The left diagram shows the correlations without excluding the influence of childrenโ€™s grades; the right diagram shows the correlations after differentiating the grades. The magnitude of the correlation is represented by the size (and color) of the circle. The corrplot package was used for drawing. [2]

Reference

[1] Espariz M, Zuljan FA, Esteban L, Magni C. Taxonomic Identity Resolution of Highly Phylogenetically Related Strains and Selection of Phylogenetic Markers by Using Genome-Scale Methods: The Bacillus pumilus Group Case. PLoS One. 2016 Sep 22;11(9):e0163098. doi: 10.1371/journal.pone.0163098. PMID: 27658251; PMCID: PMC5033322.

[2] Marx C, Hutzler F, Schuster S, Hawelka S. On the Development of Parafoveal Preprocessing: Evidence from the Incremental Boundary Paradigm. Front Psychol. 2016 Apr 14;7:514. doi: 10.3389/fpsyg.2016.00514. PMID: 27148123; PMCID: PMC4830847.

[3] Schloerke B, Cook D, Larmarange J, Briatte F, Marbach M, Thoen E, Elberg A, Crowley J (2024). GGally: Extension to โ€˜ggplot2โ€™. R package version 2.2.1, CRAN: Package GGally.

[4] Taiyun Wei and Viliam Simko (2024). R package โ€˜corrplotโ€™: Visualization of a Correlation Matrix (Version 0.94). Available from GitHub - taiyun/corrplot: A visual exploratory tool on correlation matrix

[5] Kassambara A (2023). ggcorrplot: Visualization of a Correlation Matrix using โ€˜ggplot2โ€™. R package version 0.1.4.1, CRAN: Package ggcorrplot.

[6] Wright K (2021). corrgram: Plot a Correlogram. R package version 1.14, CRAN: Package corrgram.