KMS Of Academy of mathematics and systems sciences, CAS
| 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 | 382Issue:2Pages: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 |
| 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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