Self-normalizing dual systems for minor and principal component extraction

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

In this paper classes of globally stable dynamical systems for dual-purpose extraction of principal and minor components are analyzed. The proposed systems may apply to both the standard and the generalized eigenvalue problems. Lyapunov stability theory and LaSalle invariance principle are used to derive invariant sets for these systems. Some of these systems may be viewed as generalizations of known learning rules such as Oja's and Xu's systems and are shown to be applied, with some modifications, to symmetric and nonsymmetric matrices. Numerical examples are provided to examine the convergence behavior of the dual-purpose minor and principal component analyzers.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
DOIs
StatePublished - Aug 6 2007
Event2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07 - Honolulu, HI, United States
Duration: Apr 15 2007Apr 20 2007

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume4
ISSN (Print)1520-6149

Other

Other2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
CountryUnited States
CityHonolulu, HI
Period4/15/074/20/07

Fingerprint

normalizing
Invariance
Dynamical systems
dynamical systems
learning
invariance
analyzers
eigenvalues
matrices

Keywords

  • Dual-purpose MCA/PCA systems
  • Generalized eigenvalue problem
  • Global convergence
  • Liapunov stability
  • Minor components
  • Oja's learning rule
  • Principal components
  • Rayleigh quotient

Cite this

Hasan, M. A. (2007). Self-normalizing dual systems for minor and principal component extraction. In 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07 [4218243] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 4). https://doi.org/10.1109/ICASSP.2007.367212

Self-normalizing dual systems for minor and principal component extraction. / Hasan, Mohammed A.

2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07. 2007. 4218243 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 4).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hasan, MA 2007, Self-normalizing dual systems for minor and principal component extraction. in 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07., 4218243, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 4, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, Honolulu, HI, United States, 4/15/07. https://doi.org/10.1109/ICASSP.2007.367212
Hasan MA. Self-normalizing dual systems for minor and principal component extraction. In 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07. 2007. 4218243. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2007.367212
Hasan, Mohammed A. / Self-normalizing dual systems for minor and principal component extraction. 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07. 2007. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).
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