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A generalisation of sparse PCA to multiple correspondence analysis

Abstract : Principal components analysis (PCA) for numerical variables and multiple correspondence analysis (MCA) for categorical variables are wellknown dimension reduction techniques. PCA and MCA provide a small number of informative dimensions: the components. However, these components are a combination of all original variables, hence some dif?culties in the interpretation. Factor rotation (varimax, quartimax etc.) has a long history in factor analysis for obtaining simple structure, ie looking for combinations with a large number of coef?cients either close to zero or to 1 or -1. Only recently, rotations have been used in Multiple Correspondence Analysis. Sparse PCA and group sparse PCA are new techniques providing components which are combinations of few original variables: rewriting PCA as a regression problem, null loadings are obtained by imposing the lasso (or similar) constraint on the regression coef?cients. When the data matrix has a natural block structure, group sparse PCA give zero coef?cients to entire blocks of variables. Since MCA is a special kind of PCA with blocks of indicator variables, we de?ne sparse MCA as an extension of group sparse PCA. We present an application of sparse MCA to genetic data (640 SNP?s with 3 categories measured on 502 women)and a comparison between sparse and rotated components.
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https://hal.archives-ouvertes.fr/hal-01126217
Contributor : Laboratoire Cedric <>
Submitted on : Sunday, December 13, 2020 - 11:46:01 AM
Last modification on : Tuesday, December 15, 2020 - 11:24:41 AM

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  • HAL Id : hal-01126217, version 1

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Gilbert Saporta, Anne Bernard, Christiane Guinot. A generalisation of sparse PCA to multiple correspondence analysis. ERCIM 2012, Dec 2012, Oviedo, Spain. ⟨hal-01126217⟩

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