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Conference Paper: Trace ratio vs. ratio trace for dimensionality reduction

TitleTrace ratio vs. ratio trace for dimensionality reduction
Authors
Issue Date2007
Citation
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007, article no. 4270008 How to Cite?
AbstractA large family of algorithms for dimensionality reduction end with solving a Trace Ratio problem in the form of arg maxW Tr(WTS pW)/Tr(WTSlW)1, which is generally transformed into the corresponding Ratio Trace form argmaxw Tr[ (W TSlW)-1(WTSPW) ] for obtaining a closed-form but inexact solution. In this work, an efficient iterative procedure is presented to directly solve the Trace Ratio problem. In each step, a Trace Difference problem arg maxiv Tr[WT(Sp - λSl)W] is solved with X being the trace ratio value computed from the previous step. Convergence of the projection matrix W, as well as the global optimum of the trace ratio value λ, are proven based on point-to-set map theories. In addition, this procedure is further extended for solving trace ratio problems with more general constraint WTCW=I and providing exact solutions for kernel-based subspace learning problems. Extensive experiments on faces and UCI data demonstrate the high convergence speed of the proposed solution, as well as its superiority in classification capability over corresponding solutions to the ratio trace problem. ©2007 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/321328
ISSN
2023 SCImago Journal Rankings: 10.331

 

DC FieldValueLanguage
dc.contributor.authorWang, Huan-
dc.contributor.authorYan, Shuicheng-
dc.contributor.authorXu, Dong-
dc.contributor.authorTang, Xiaoou-
dc.contributor.authorHuang, Thomas-
dc.date.accessioned2022-11-03T02:18:11Z-
dc.date.available2022-11-03T02:18:11Z-
dc.date.issued2007-
dc.identifier.citationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007, article no. 4270008-
dc.identifier.issn1063-6919-
dc.identifier.urihttp://hdl.handle.net/10722/321328-
dc.description.abstractA large family of algorithms for dimensionality reduction end with solving a Trace Ratio problem in the form of arg maxW Tr(WTS pW)/Tr(WTSlW)1, which is generally transformed into the corresponding Ratio Trace form argmaxw Tr[ (W TSlW)-1(WTSPW) ] for obtaining a closed-form but inexact solution. In this work, an efficient iterative procedure is presented to directly solve the Trace Ratio problem. In each step, a Trace Difference problem arg maxiv Tr[WT(Sp - λSl)W] is solved with X being the trace ratio value computed from the previous step. Convergence of the projection matrix W, as well as the global optimum of the trace ratio value λ, are proven based on point-to-set map theories. In addition, this procedure is further extended for solving trace ratio problems with more general constraint WTCW=I and providing exact solutions for kernel-based subspace learning problems. Extensive experiments on faces and UCI data demonstrate the high convergence speed of the proposed solution, as well as its superiority in classification capability over corresponding solutions to the ratio trace problem. ©2007 IEEE.-
dc.languageeng-
dc.relation.ispartofProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition-
dc.titleTrace ratio vs. ratio trace for dimensionality reduction-
dc.typeConference_Paper-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1109/CVPR.2007.382983-
dc.identifier.scopuseid_2-s2.0-35148823228-
dc.identifier.spagearticle no. 4270008-
dc.identifier.epagearticle no. 4270008-

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