Learning linear PCA with convex semi-definite programming

	Learning linear PCA with convex semi-definite programming
	Tao, Qing ; Wu, Gao-wei ; Wang, Jue
刊名	PATTERN RECOGNITION
	2007-10-01
卷号	40 期号:10 页码:2633-2640
关键词	principal component analysis statistical learning theory support vector machines margin maximal margin algorithm semi-definite programming robustness
英文摘要	The 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.
WOS标题词	Science & Technology ; Technology
类目[WOS]	Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
研究领域[WOS]	Computer Science ; Engineering
关键词[WOS]	PRINCIPAL COMPONENT ANALYSIS ; MATRIX
收录类别	SCI
语种	英语
WOS记录号	WOS:000247650000003
公开日期	2015-12-24
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/9410]
专题	自动化研究所_09年以前成果
作者单位	1.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
推荐引用方式 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.