Weighted Rayleigh quotients for minor and principal component extraction

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationProceedings of the International Joint Conference on Neural Networks, IJCNN 2005
Pages1263-1268
Number of pages6
DOIs
StatePublished - Dec 1 2005
EventInternational Joint Conference on Neural Networks, IJCNN 2005 - Montreal, QC, Canada
Duration: Jul 31 2005Aug 4 2005

Publication series

NameProceedings of the International Joint Conference on Neural Networks
Volume2

Other

OtherInternational Joint Conference on Neural Networks, IJCNN 2005
CountryCanada
CityMontreal, QC
Period7/31/058/4/05

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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  • Cite this

    Hasan, M. A. (2005). Weighted Rayleigh quotients for minor and principal component extraction. In Proceedings of the International Joint Conference on Neural Networks, IJCNN 2005 (pp. 1263-1268). [1556035] (Proceedings of the International Joint Conference on Neural Networks; Vol. 2). https://doi.org/10.1109/IJCNN.2005.1556035