Dual systems for minor and principal component computation

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

2 Scopus citations

Abstract

Converting principal component dynamical system to a minor component dynamical system and vice versa sometimes leads to unstable systems. In this paper, classes of globally stable dynamical systems that can be converted between PCA and MCA systems by merely switching the signs of some terms of a given system are developed. These systems are shown to be applicable to symmetric and nonsymmetric matrices. These systems are then modified to be asymptotically stable by adding a penalty term. 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.

Original languageEnglish (US)
Title of host publication2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Pages1901-1904
Number of pages4
DOIs
StatePublished - Sep 16 2008
Event2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP - Las Vegas, NV, United States
Duration: Mar 31 2008Apr 4 2008

Publication series

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

Other

Other2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
CountryUnited States
CityLas Vegas, NV
Period3/31/084/4/08

Keywords

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

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