Analysis of dynamical systems for generalized principal and minor component extraction

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

2 Scopus citations

Abstract

In this paper globally stable dynamical systems for the standard and the generalized eigenvalue problem are developed. These systems may be viewed as generalizations of known learning rules applied to nondefinite and/or nonsymmetric matrices. We also modified the original Oja's systems to obtain new dynamical systems with a larger domain of attraction. For certain class of matrices which satisfy positive definiteness condition, the modified rules are globally stable. The convergence behavior has been examined to identify the stationarity conditions, stability conditions, and domains of attraction for some of these systems.

Original languageEnglish (US)
Title of host publication2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006
Pages531-535
Number of pages5
StatePublished - Dec 1 2006
Event4th IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006 - Waltham, MA, United States
Duration: Jul 12 2006Jul 14 2006

Publication series

Name2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006

Other

Other4th IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006
CountryUnited States
CityWaltham, MA
Period7/12/067/14/06

Keywords

  • Extreme eigenvalues
  • Generalized eigenvalue problem
  • Global behavior
  • Global convergence
  • Leftmost and rightmost invariant subspaces
  • Liapunov stability
  • Oja's learning rule
  • Optimization on manifolds
  • Rayleigh quotient

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