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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Yitzhaki, S. & E. Schechtman (2013) The Gini Methodology. A Primer on a Statistical Methodology | 1.000 | 8 | 4 | 100% |
| 2 | Banerjee, A.K (2010) A multidimensional Gini index | 0.928 | 4 | 3 | 100% |
| 3 | Schechtman, E. & S. Yitzhaki (2003) A family of correlation coefficients based on the extended Gini index | 0.811 | 4 | 2 | 100% |
| 4 | Schechtman, E. & S. Yitzhaki (1987) A Measure of Association Based on Gini's Mean Difference | 0.737 | 3 | 2 | 100% |
| 5 | \ Yaari, M.E (1987) The Dual Theory of Choice Under Risk | 0.737 | 3 | 2 | 100% |
| 6 | Gini, C (1912) Variabilità e mutabilità, Memori di Metodologia Statistica, Vol | 0.644 | 2 | 2 | 100% |
| 7 | Korhonen, P. & Siljamäki, A (1998) Ordinal principal component analysis theory and an application | 0.644 | 2 | 2 | 100% |
| 8 | \ Yaari, M.E (1988) A Controversial Proposal Concerning Inequality Measurement | 0.511 | 2 | 1 | 100% |
| 9 | Abramowitz, M. & I. Stegun (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables | 0.405 | 1 | 1 | 100% |
| 10 | Anderson, T.W (1963) Asymptotic Theory for Principal Component Analysis | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 36 scored citations.