Recursive estimation for ordered eigenvectors of symmetric matrix with observation noise

doi:10.1016/j.jmaa.2011.04.072

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	Recursive estimation for ordered eigenvectors of symmetric matrix with observation noise
	Chen, Han-Fu; Fang, Hai-Tao; Zhang, Li-Li
	2011-10-15
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	382 期号:2 页码:822-842
摘要	The principal component analysis is to recursively estimate the eigenvectors and the corresponding eigenvalues of a symmetric matrix A based on its noisy observations A(k) = A + N-k, where A is allowed to have arbitrary eigenvalues with multiplicity possibly bigger than one. In the paper the recursive algorithms are proposed and their ordered convergence is established: It is shown that the first algorithm as. converges to a unit eigenvector corresponding to the largest eigenvalue, the second algorithm as. converges to a unit eigenvector corresponding to either the second largest eigenvalue in the case the largest eigenvalue is of single multiplicity or the largest eigenvalue if the multiplicity of the largest eigenvalue is bigger than one, and so on. The convergence rate is also derived. (C) 2011 Elsevier Inc. All rights reserved.
关键词	Principal component analysis (PCA) Recursive algorithm Stochastic approximation Ordered convergence Convergence rate
DOI	10.1016/j.jmaa.2011.04.072
语种	英语
资助项目	NSFC[60821091] ; NSFC[60874001] ; NSFC[60221301] ; NSFC[60774020] ; National Laboratory of Space Intelligent Control
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000291714400027
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12438
专题	系统科学研究所
通讯作者	Chen, Han-Fu
作者单位	Chinese Acad Sci, Key Lab Syst & Control, Inst Syst Sci, AMSS, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, Han-Fu,Fang, Hai-Tao,Zhang, Li-Li. Recursive estimation for ordered eigenvectors of symmetric matrix with observation noise[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2011,382(2):822-842.
APA	Chen, Han-Fu,Fang, Hai-Tao,&Zhang, Li-Li.(2011).Recursive estimation for ordered eigenvectors of symmetric matrix with observation noise.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,382(2),822-842.
MLA	Chen, Han-Fu,et al."Recursive estimation for ordered eigenvectors of symmetric matrix with observation noise".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 382.2(2011):822-842.