Learning linear PCA with convex semi-definite programming

doi:10.1016/j.patcog.2007.01.022

	Learning linear PCA with convex semi-definite programming
	Tao, Qing ; Wu, Gao-wei ; Wang, Jue
	2007-10-01
发表期刊	PATTERN RECOGNITION
ISSN	0031-3203
卷号	40 期号:10 页码:2633-2640
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.
关键词	principal component analysis statistical learning theory support vector machines margin maximal margin algorithm semi-definite programming robustness
DOI	10.1016/j.patcog.2007.01.022
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS记录号	WOS:000247650000003
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计	被引频次：6[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/10865
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Tao, Qing
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.