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Conference Paper: Generalized principal component analysis (GPCA)

TitleGeneralized principal component analysis (GPCA)
Authors
Issue Date2003
Citation
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003, v. 1 How to Cite?
AbstractWe propose an algebraic geometric approach to the problem of estimating a mixture of linear subspaces from sample data points, the so-called Generalized Principal Component Analysis (GPCA) problem. In the absence of noise, we show that GPCA is equivalent to factoring a homogeneous polynomial whose degree is the number of subspaces and whose factors (roots) represent normal vectors to each subspace. We derive a formula for the number of subspaces n and provide an analytic solution to the factorization problem using linear algebraic techniques. The solution is closed form if and only if n ≤ 4. In the presence of noise, we cast GPCA as a constrained nonlinear least squares problem and derive an optimal function from which the subspaces can be directly recovered using standard nonlinear optimization techniques. We apply GPCA to the motion segmentation problem in computer vision, i.e. the problem of estimating a mixture of motion models from 2-D imagery.
Persistent Identifierhttp://hdl.handle.net/10722/326753
ISSN
2023 SCImago Journal Rankings: 10.331

 

DC FieldValueLanguage
dc.contributor.authorVidal, René-
dc.contributor.authorMa, Yi-
dc.contributor.authorSastry, Shankar-
dc.date.accessioned2023-03-31T05:26:16Z-
dc.date.available2023-03-31T05:26:16Z-
dc.date.issued2003-
dc.identifier.citationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003, v. 1-
dc.identifier.issn1063-6919-
dc.identifier.urihttp://hdl.handle.net/10722/326753-
dc.description.abstractWe propose an algebraic geometric approach to the problem of estimating a mixture of linear subspaces from sample data points, the so-called Generalized Principal Component Analysis (GPCA) problem. In the absence of noise, we show that GPCA is equivalent to factoring a homogeneous polynomial whose degree is the number of subspaces and whose factors (roots) represent normal vectors to each subspace. We derive a formula for the number of subspaces n and provide an analytic solution to the factorization problem using linear algebraic techniques. The solution is closed form if and only if n ≤ 4. In the presence of noise, we cast GPCA as a constrained nonlinear least squares problem and derive an optimal function from which the subspaces can be directly recovered using standard nonlinear optimization techniques. We apply GPCA to the motion segmentation problem in computer vision, i.e. the problem of estimating a mixture of motion models from 2-D imagery.-
dc.languageeng-
dc.relation.ispartofProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition-
dc.titleGeneralized principal component analysis (GPCA)-
dc.typeConference_Paper-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-5044234987-
dc.identifier.volume1-

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