gcor package for R

gcor is an R package which provides tools for multivariate data analysis based on a generalized correlation measure.

It features a generalized version of (absolute) correlation coefficient for arbitrary types of data, including both numerical and categorical variables. Missing values can also be handled naturally by treating them as observations of a categorical value NA.

Installation

CRAN

install.packages("gcor")

GitHub (development version)

# install.packages("pak")
pak::pak("r-suzuki/gcor-r")

or

# install.packages("devtools")
devtools::install_github("r-suzuki/gcor-r")

Documentation

Method Overview

• English
• Japanese

Examples

library(gcor)

Generalized correlation measure takes values in $[0,1]$, which can capture both linear and nonlinear relations.

When the joint distribution of $(X,Y)$ is bivariate normal, its theoretical value coincides with the absolute value of the correlation coefficient.

# Generalized correlation measure
gcor(iris)
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
#> Sepal.Length    1.0000000   0.2349075    0.8846517   0.8741873 0.7718469
#> Sepal.Width     0.2349075   1.0000000    0.3143301   0.2669031 0.6591442
#> Petal.Length    0.8846517   0.3143301    1.0000000   0.9503289 0.8323583
#> Petal.Width     0.8741873   0.2669031    0.9503289   1.0000000 0.8339534
#> Species         0.7718469   0.6591442    0.8323583   0.8339534 1.0000000

The directed generalized correlation is another variation of the generalized correlation. It also takes values in $[0,1]$, reaching $1$ when $Y$ is completely dependent on $X$ (i.e., when the conditional distribution $f(Y \mid X)$ is a one-point distribution) and $0$ when $X$ and $Y$ are independent.

# Dependency of Species on other variables
dgc <- dgcor(Species ~ ., data = iris)
dotchart(sort(dgc), main = "Dependency of Species")

With $r_g$ as the generalized correlation between $X$ and $Y$, we can define a dissimilarity measure:

$$ d(X,Y) = \sqrt{1 - r^2_g} $$

It can be applied to cluster analysis:

# Clustering
gd <- gdis(iris)
hc <- hclust(gd, method = "ward.D2")
plot(hc)

Multidimensional scaling would serve as a good example of an application:

# Multidimensional scaling
mds <- cmdscale(gd, k = 2)
plot(mds, type = "n", xlab = "", ylab = "", asp = 1, axes = FALSE,
     main = "cmdscale with gdis(iris)")
text(mds[,1], mds[,2], rownames(mds))