Principal Component Analysis: A Generalized Gini Approach

Arthur Charpentier (), Stéphane Mussard and Tea Ouraga
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Arthur Charpentier: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, UQAM - Université du Québec à Montréal = University of Québec in Montréal
Tea Ouraga: CHROME - Détection, évaluation, gestion des risques CHROniques et éMErgents (CHROME) - Université de Nîmes - UNIMES - Université de Nîmes

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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 out-liers. 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.

Keywords: Generalized Gini; PCA; Robustness (search for similar items in EconPapers)
Date: 2019-10-22
Note: View the original document on HAL open archive server: https://hal.science/hal-02327521v1
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Principal component analysis: A generalized Gini approach (2021)
Working Paper: Principal Component Analysis: A Generalized Gini Approach (2019)
Working Paper: Principal Component Analysis: A Generalized Gini Approach (2019)
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