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Principal Component Analysis: A Generalized Gini Approach

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.
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Preprints, Working Papers, ...
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Contributor : Arthur Charpentier Connect in order to contact the contributor
Submitted on : Tuesday, October 22, 2019 - 7:35:12 PM
Last modification on : Thursday, March 24, 2022 - 3:38:16 AM
Long-term archiving on: : Thursday, January 23, 2020 - 10:11:15 PM


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  • HAL Id : hal-02327521, version 1


Arthur Charpentier, Stéphane Mussard, Tea Ouraga. Principal Component Analysis: A Generalized Gini Approach. 2019. ⟨hal-02327521⟩



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