Joint computation of principal and minor components using gradient dynamical systems over stiefel manifolds

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

2 Scopus citations

Abstract

This paper presents several dynamical systems for simultaneous computation of principal and minor subspaces of a symmetric matrix. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Necessary optimality conditions are given in terms of a gradient of certain cost functions over a Stiefel manifold. Stability analysis of equilibrium points of six algorithms is established using Liapunov direct method.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages3287-3292
Number of pages6
DOIs
StatePublished - 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

Keywords

  • Eigenvalue spread
  • Gradient dynamical systems
  • Joint PCA-MCA
  • Joint PSA-MSA
  • Oja's rule
  • Stiefel manifold

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