Weighted Rayleigh quotients for minor and principal component extraction

Mohammed A. Hasan

doi:10.1109/IJCNN.2005.1556035

Weighted Rayleigh quotients for minor and principal component extraction

Mohammed A. Hasan

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

New criteria are proposed for extracting in parallel multiple minor and principal components associated with the co-variance matrix of an input process. The proposed minor and principal component analyzer (MCA/PCA) algorithms are based on optimizing a weighted inverse Rayleigh quotient so that the optimum equilibrium points are exactly the desired eigenvectors of a covariance matrix instead of an arbitrary orthonormal basis of the minor subspace. Variations of the derived MCA/PCA learning rules are obtained by imposing orthogonal and quadratic constraints and change of variables. Similar criteria are proposed for component analysis of the generalized eigenvalue problem. Some of the proposed MCA algorithms can also perform PCA by merely changing the sign of the step-size. These algorithms may be seen as generalization of Oja's and Xu's systems for computing multiple principal components.

Original language	English (US)
Title of host publication	Proceedings of the International Joint Conference on Neural Networks, IJCNN 2005
Pages	1263-1268
Number of pages	6
DOIs	https://doi.org/10.1109/IJCNN.2005.1556035
State	Published - 2005
Event	International Joint Conference on Neural Networks, IJCNN 2005 - Montreal, QC, Canada Duration: Jul 31 2005 → Aug 4 2005

Publication series

Name	Proceedings of the International Joint Conference on Neural Networks
Volume	2

Other

Other	International Joint Conference on Neural Networks, IJCNN 2005
Country/Territory	Canada
City	Montreal, QC
Period	7/31/05 → 8/4/05

Bibliographical note

Funding Information:
Intergovernmental Forum on Chemical Safety (IFCS) Web: http://www.who.int/ifcs/forums/four/video/en/index.html Chemical Safety in a Vulnerable World Toxicology Education Foundation, TEF Web: http://www.toxedfoundation.org/ Is it Safe? Evaluating Chemical Risks (produced by the Toxicology Education Foundation, TEF and co-sponsored by the U.S. National Institute of Environmental Health Sciences, NIEHS) (available in English and Latin American Spanish, with a Japanese version in process). Video Jug Web: http://www.videojug.com/tag/toxicology Toxicology: With Dr. Barry Ginsberg

Keywords

Adaptive learning algorithm
Extreme eigenvalues
Generalized Rayleigh quotient
Minor component analysis
Neural networks
Principal component analysis
Weighted Rayleigh quotient
Weighted inverse Rayleigh quotient

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10.1109/IJCNN.2005.1556035

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Weighted Rayleigh quotients for minor and principal component extraction. / Hasan, Mohammed A.
Proceedings of the International Joint Conference on Neural Networks, IJCNN 2005. 2005. p. 1263-1268 1556035 (Proceedings of the International Joint Conference on Neural Networks; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hasan, MA 2005, Weighted Rayleigh quotients for minor and principal component extraction. in Proceedings of the International Joint Conference on Neural Networks, IJCNN 2005., 1556035, Proceedings of the International Joint Conference on Neural Networks, vol. 2, pp. 1263-1268, International Joint Conference on Neural Networks, IJCNN 2005, Montreal, QC, Canada, 7/31/05. https://doi.org/10.1109/IJCNN.2005.1556035

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Weighted Rayleigh quotients for minor and principal component extraction

Abstract

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Bibliographical note

Keywords

Access

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