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Principal Component Analysis A Generalized Gini Approach

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Document pages: 39 pages

Abstract: A principal component analysis based on the generalized Gini correlationindex is proposed (Gini PCA). The Gini PCA generalizes the standard PCA basedon the variance. It is shown, in the Gaussian case, that the standard PCA isequivalent to the Gini PCA. It is also proven that the dimensionality reductionbased on the generalized Gini correlation matrix, that relies on city-blockdistances, is robust to outliers. Monte Carlo simulations and an application oncars data (with outliers) show the robustness of the Gini PCA and providedifferent interpretations of the results compared with the variance PCA.

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