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Principal component analysis: A generalized Gini approach

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  • Charpentier, Arthur
  • Mussard, Stéphane
  • Ouraga, Téa

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.

Suggested Citation

  • Charpentier, Arthur & Mussard, Stéphane & Ouraga, Téa, 2021. "Principal component analysis: A generalized Gini approach," European Journal of Operational Research, Elsevier, vol. 294(1), pages 236-249.
    • Handle: RePEc:eee:ejores:v:294:y:2021:i:1:p:236-249
    DOI: 10.1016/j.ejor.2021.02.010
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    2. Vasile Preda & Luigi-Ionut Catana, 2021. "Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders," Mathematics, MDPI, vol. 9(11), pages 1-22, May.

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