Principal Component Analysis: A Generalized Gini Approach

TL;DR

This paper introduces Gini PCA, a robust alternative to standard PCA based on the generalized Gini correlation index, which is less sensitive to outliers and offers new interpretative insights.

Contribution

It proposes a Gini PCA method that generalizes variance-based PCA, demonstrating robustness to outliers and providing a new perspective on dimensionality reduction.

Findings

Gini PCA is equivalent to standard PCA in Gaussian cases.

Gini PCA is robust to outliers due to city-block distance reliance.

Monte Carlo simulations confirm robustness and interpretative differences.

Abstract

A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation matrix, that relies on city-block distances, is robust to outliers. Monte Carlo simulations and an application on cars data (with outliers) show the robustness of the Gini PCA and provide different interpretations of the results compared with the variance PCA.