Dynamical systems for principal singular subspace analysis

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

4 Scopus citations

Abstract

The computation of the principal subspaces is an essential task in many signal processing and control applications. In this paper novel dynamical systems for finding the principal singular subspace and/or components of arbitrary matrix are developed. The proposed dynamical systems are gradient flows or weighted gradient flows derived from the optimization of certain objective functions over orthogonal constraints. Global asymptotic stability analysis and domains of attractions of these systems are examined via Liapunov theory and LaSalle invariance principle. Weighted versions of these methods for computing principal singular components are also given. Qualitative properties of the proposed systems are analyzed in detail.

Original languageEnglish (US)
Title of host publication2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006
Pages142-146
Number of pages5
DOIs
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

  • Asymptotic stability
  • Constrained optimization
  • Global convergence
  • Gradient flow
  • Invariant set
  • Lasalle invariance principle
  • Principal singular flow
  • SVD
  • Stiefel manifold

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