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Group-sparse block PCA and explained variance

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorCHAVENT, Marie
hal.structure.identifierSimulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]
dc.contributor.authorCHAVENT, Guy
dc.date.accessioned2024-04-04T03:07:36Z
dc.date.available2024-04-04T03:07:36Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193457
dc.description.abstractEnThe 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.
dc.language.isoen
dc.title.enGroup-sparse block PCA and explained variance
dc.typeDocument de travail - Pré-publication
dc.subject.halStatistiques [stat]/Autres [stat.ML]
dc.identifier.arxiv1705.00461
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01662605
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01662605v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=CHAVENT,%20Marie&CHAVENT,%20Guy&rft.genre=preprint


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