Covariance and PCA for Categorical Variables

TL;DR

This paper introduces a novel covariance measure for categorical variables based on regular simplex expressions and proposes a PCA method (RS-PCA) that enhances interpretability and aids variable selection in categorical datasets.

Contribution

It presents a new covariance definition for categorical data and a PCA method using regular simplex expressions, improving interpretability and variable selection.

Findings

Reasonable covariance values for test data

RS-PCA enhances interpretability of principal components

Effective variable selection criterion for categorical data

Abstract

Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated results give reasonable values for test data. A method of principal component analysis (RS-PCA) is also proposed using regular simplex expressions, which allows easy interpretation of the principal components. The proposed methods apply to variable selection problem of categorical data USCensus1990 data. The proposed methods give appropriate criterion for the variable selection problem of categorical