Group-sparse block PCA and explained variance

Abstract : The paper addresses the simultneous determination of goup-sparse loadings by block optimization, and the correlated problem of defining explained variance for a set of non orthogonal components. We give in both cases a comprehensive mathematical presentation of the problem, which leads to propose i) a new formulation/algorithm for group-sparse block PCA and ii) a framework for the definition of explained variance with the analysis of five definitions. The numerical results i) confirm the superiority of block optimization over deflation for the determination of group-sparse loadings, and the importance of group information when available, and ii) show that ranking of algorithms according to explained variance is essentially independant of the definition of explained variance. These results lead to propose a new optimal variance as the definition of choice for explained variance.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01662605
Contributeur : Marie Chavent <>
Soumis le : mercredi 13 décembre 2017 - 12:02:40
Dernière modification le : jeudi 26 avril 2018 - 10:28:45

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  • HAL Id : hal-01662605, version 1
  • ARXIV : 1705.00461

Citation

Marie Chavent, Guy Chavent. Group-sparse block PCA and explained variance. 2017. 〈hal-01662605〉

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