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Principal Component Analysis: A Generalized Gini Approach

Charpentier, Arthur, Mussard, Stephane, Tea Ouraga

arXiv 22 Oct 2019 · Statistics — Methodology · publishedEuropean Journal of Operational Research (2021) · 14 citations (OpenAlex)

arXiv:1910.10133 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

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appendix boundary found by appendix_titled_section at “Appendix” · 99% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Yitzhaki, S. & E. Schechtman (2013) The Gini Methodology. A Primer on a Statistical Methodology1.00084100%
2Banerjee, A.K (2010) A multidimensional Gini index0.92843100%
3Schechtman, E. & S. Yitzhaki (2003) A family of correlation coefficients based on the extended Gini index0.81142100%
4Schechtman, E. & S. Yitzhaki (1987) A Measure of Association Based on Gini's Mean Difference0.73732100%
5\ Yaari, M.E (1987) The Dual Theory of Choice Under Risk0.73732100%
6Gini, C (1912) Variabilità e mutabilità, Memori di Metodologia Statistica, Vol0.64422100%
7Korhonen, P. & Siljamäki, A (1998) Ordinal principal component analysis theory and an application0.64422100%
8\ Yaari, M.E (1988) A Controversial Proposal Concerning Inequality Measurement0.51121100%
9Abramowitz, M. & I. Stegun (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables0.40511100%
10Anderson, T.W (1963) Asymptotic Theory for Principal Component Analysis0.40511100%

Showing the top 10 of 36 scored citations.