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Article: Generalized principal component analysis (GPCA)

TitleGeneralized principal component analysis (GPCA)
Authors
KeywordsDimensionality reduction
Dynamic scenes and motion segmentation
Principal component analysis (PCA)
Subspace segmentation
Temporal video segmentation
Veronese map
Issue Date2005
Citation
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, v. 27, n. 12, p. 1945-1959 How to Cite?
AbstractThis paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views. © 2005 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/326699
ISSN
2023 Impact Factor: 20.8
2023 SCImago Journal Rankings: 6.158
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorVidal, René-
dc.contributor.authorMa, Yi-
dc.contributor.authorSastry, Shankar-
dc.date.accessioned2023-03-31T05:25:53Z-
dc.date.available2023-03-31T05:25:53Z-
dc.date.issued2005-
dc.identifier.citationIEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, v. 27, n. 12, p. 1945-1959-
dc.identifier.issn0162-8828-
dc.identifier.urihttp://hdl.handle.net/10722/326699-
dc.description.abstractThis paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views. © 2005 IEEE.-
dc.languageeng-
dc.relation.ispartofIEEE Transactions on Pattern Analysis and Machine Intelligence-
dc.subjectDimensionality reduction-
dc.subjectDynamic scenes and motion segmentation-
dc.subjectPrincipal component analysis (PCA)-
dc.subjectSubspace segmentation-
dc.subjectTemporal video segmentation-
dc.subjectVeronese map-
dc.titleGeneralized principal component analysis (GPCA)-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1109/TPAMI.2005.244-
dc.identifier.pmid16355661-
dc.identifier.scopuseid_2-s2.0-30144438432-
dc.identifier.volume27-
dc.identifier.issue12-
dc.identifier.spage1945-
dc.identifier.epage1959-
dc.identifier.isiWOS:000232532600009-

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