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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 PublicationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN0022-247X
Volume382Issue:2Pages:822-842
AbstractThe 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.
KeywordPrincipal component analysis (PCA) Recursive algorithm Stochastic approximation Ordered convergence Convergence rate
DOI10.1016/j.jmaa.2011.04.072
Language英语
Funding ProjectNSFC[60821091] ; NSFC[60874001] ; NSFC[60221301] ; NSFC[60774020] ; National Laboratory of Space Intelligent Control
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000291714400027
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12438
Collection系统科学研究所
AffiliationChinese 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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