Principal component analysis: A generalized Gini approach

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. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

The Gini PCA, based on the generalized Gini correlation index, is proposed as a method for robust dimensionality reduction that is shown to be equivalent to standard PCA in the Gaussian case. Monte Carlo simulations and application on cars data demonstrate the robustness and different interpretations of results compared to variance PCA.