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
Source Publication	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
Volume	382 Issue:2 Pages:822-842
Abstract	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.
Keyword	Principal component analysis (PCA) Recursive algorithm Stochastic approximation Ordered convergence Convergence rate
DOI	10.1016/j.jmaa.2011.04.072
Language	英语
Funding Project	NSFC[60821091] ; NSFC[60874001] ; NSFC[60221301] ; NSFC[60774020] ; National Laboratory of Space Intelligent Control
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000291714400027
Publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/12438
Collection	系统科学研究所
Corresponding Author	Chen, Han-Fu
Affiliation	Chinese Acad Sci, Key Lab Syst & Control, Inst Syst Sci, AMSS, Beijing 100080, Peoples R China
Recommended Citation 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.

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