Low-rank approximations with applications to principal singular component learning systems

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

6 Scopus citations

Abstract

In this paper, we present several dynamical systems for efficient and accurate computation of optimal low rank approximation of a real matrix. The proposed dynamical systems are gradient flows or weighted gradient flows derived from unconstrained optimization of certain objective functions. These systems are then modified to obtain power-like methods for computing a few dominant singular triplets of very large matrices simultaneously rather than just one at a time, by incorporating upper-triangular and diagonal matrices. The validity of the proposed algorithms was demonstrated through numerical experiments.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages3293-3298
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

  • Asymptotic stability
  • Constrained optimization
  • Dynamical system
  • Global convergence
  • Principal singular flow
  • SVD
  • Stiefel manifold

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