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Learning linear PCA with convex semi-definite programming
Tao, Qing; Wu, Gao-wei; Wang, Jue
AbstractThe aim of this paper is to learn a linear principal component using the nature of support vector machines (SVMs). To this end, a complete SVM-like framework of linear PCA (SVPCA) for deciding the projection direction is constructed, where new expected risk and margin are introduced. Within this framework, a new semi-definite programming problem for maximizing the margin is formulated and a new definition of support vectors is established. As a weighted case of regular PCA, our SVPCA coincides with the regular PCA if all the samples play the same part in data compression. Theoretical explanation indicates that SVPCA is based on a margin-based generalization bound and thus good prediction ability is ensured. Furthermore, the robust form of SVPCA with a interpretable parameter is achieved using the soft idea in SVMs. The great advantage lies in the fact that SVPCA is a learning algorithm without local minima because of the convexity of the semi-definite optimization problems. To validate the performance of SVPCA, several experiments are conducted and numerical results have demonstrated that their generalization ability is better than that of regular PCA. Finally, some existing problems are also discussed. (c) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
KeywordPrincipal Component Analysis Statistical Learning Theory Support Vector Machines Margin Maximal Margin Algorithm Semi-definite Programming Robustness
WOS HeadingsScience & Technology ; Technology
Indexed BySCI
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000247650000003
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Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Chinese Acad Sci, Inst Automat, Lab Complex Syst & Intelligence Sci, Beijing 100080, Peoples R China
2.New Star Res Inst Appl Tech, Hefei 230031, Peoples R China
3.Chinese Acad Sci, Inst Comp Technol, Div Intelligent Software Syst, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Tao, Qing,Wu, Gao-wei,Wang, Jue. Learning linear PCA with convex semi-definite programming[J]. PATTERN RECOGNITION,2007,40(10):2633-2640.
APA Tao, Qing,Wu, Gao-wei,&Wang, Jue.(2007).Learning linear PCA with convex semi-definite programming.PATTERN RECOGNITION,40(10),2633-2640.
MLA Tao, Qing,et al."Learning linear PCA with convex semi-definite programming".PATTERN RECOGNITION 40.10(2007):2633-2640.
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