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Conference Paper: Minimum effective dimension for mixtures of subspaces: A robust GPCA algorithm and its applications

TitleMinimum effective dimension for mixtures of subspaces: A robust GPCA algorithm and its applications
Authors
Issue Date2004
Citation
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004, v. 2 How to Cite?
AbstractIn this paper, we propose a robust model selection criterion for mixtures ofsubspaces called minimum effective dimension (MED). Previous information-theoretic model selection criteria typically assume that data can be modelled with a parametric model of certain (possibly differing) dimension and a known error distribution. However, for mixtures of subspaces with different dimensions, a generalized notion of dimensionality is needed and hence introduced in this paper. The proposed MED criterion minimizes this geometric dimension subject to a given error tolerance (regardless of the noise distribution). Furthermore, combined with a purely algebraic approach to clustering mixtures of sub-spaces, namely the Generalized PCA (GPCA), the MED is designed to also respect the global algebraic and geometric structure of the data. The result is a non-iterative algorithm called robust GPCA that estimates from noisy data an unknown number of subspaces with unknown and possibly different dimensions subject to a maximum error bound. We test the algorithm on synthetic noisy data and in applications such as motion/image/video segmentation.
Persistent Identifierhttp://hdl.handle.net/10722/326751
ISSN
2023 SCImago Journal Rankings: 10.331

 

DC FieldValueLanguage
dc.contributor.authorHuang, Kun-
dc.contributor.authorMa, Yi-
dc.contributor.authorVidal, René-
dc.date.accessioned2023-03-31T05:26:16Z-
dc.date.available2023-03-31T05:26:16Z-
dc.date.issued2004-
dc.identifier.citationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004, v. 2-
dc.identifier.issn1063-6919-
dc.identifier.urihttp://hdl.handle.net/10722/326751-
dc.description.abstractIn this paper, we propose a robust model selection criterion for mixtures ofsubspaces called minimum effective dimension (MED). Previous information-theoretic model selection criteria typically assume that data can be modelled with a parametric model of certain (possibly differing) dimension and a known error distribution. However, for mixtures of subspaces with different dimensions, a generalized notion of dimensionality is needed and hence introduced in this paper. The proposed MED criterion minimizes this geometric dimension subject to a given error tolerance (regardless of the noise distribution). Furthermore, combined with a purely algebraic approach to clustering mixtures of sub-spaces, namely the Generalized PCA (GPCA), the MED is designed to also respect the global algebraic and geometric structure of the data. The result is a non-iterative algorithm called robust GPCA that estimates from noisy data an unknown number of subspaces with unknown and possibly different dimensions subject to a maximum error bound. We test the algorithm on synthetic noisy data and in applications such as motion/image/video segmentation.-
dc.languageeng-
dc.relation.ispartofProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition-
dc.titleMinimum effective dimension for mixtures of subspaces: A robust GPCA algorithm and its applications-
dc.typeConference_Paper-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-5044226698-
dc.identifier.volume2-

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