Show simple item record

Geometry-aware principal component analysis for symmetric positive definite matrices

hal.structure.identifierUniversity of Tokyo
dc.contributor.authorHorev, Inbal
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorYger, Florian
HAL ID: 17768
ORCID: 0000-0002-7182-8062
hal.structure.identifierUniversity of Tokyo
dc.contributor.authorSugiyama, Masashi
dc.date.accessioned2017-03-07T12:53:49Z
dc.date.available2017-03-07T12:53:49Z
dc.date.issued2016
dc.identifier.issn0885-6125
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16293
dc.language.isoenen
dc.subjectdimensionality reductionen
dc.subjectPCAen
dc.subjectRiemannian geometryen
dc.subjectSPD manifolden
dc.subjectGrassmann manifolden
dc.subject.ddc516; 519en
dc.titleGeometry-aware principal component analysis for symmetric positive definite matricesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenSymmetric positive definite (SPD) matrices in the form of covariance matrices, for example, are ubiquitous in machine learning applications. However, because their size grows quadratically with respect to the number of variables, high-dimensionality can pose a difficulty when working with them. So, it may be advantageous to apply to them dimensionality reduction techniques. Principal component analysis (PCA) is a canonical tool for dimensionality reduction, which for vector data maximizes the preserved variance. Yet, the commonly used, naive extensions of PCA to matrices result in sub-optimal variance retention. Moreover, when applied to SPD matrices, they ignore the geometric structure of the space of SPD matrices, further degrading the performance. In this paper we develop a new Riemannian geometry based formulation of PCA for SPD matrices that (1) preserves more data variance by appropriately extending PCA to matrix data, and (2) extends the standard definition from the Euclidean to the Riemannian geometries. We experimentally demonstrate the usefulness of our approach as pre-processing for EEG signals and for texture image classification.en
dc.relation.isversionofjnlnameMachine Learning
dc.relation.isversionofjnldate2016-11
dc.relation.isversionofjnlpages1-30en
dc.relation.isversionofdoi10.1007/s10994-016-5605-5en
dc.contributor.countryeditoruniversityotherJAPAN
dc.subject.ddclabelGéométrie; Probabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-07T12:41:15Z
hal.identifierhal-01484571*
hal.version1*
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record