Stability analysis of dynamical systems for minor and principal component analysis

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

1 Scopus citations


Algorithms that extract the principal or minor components of a signal are widely used in signal processing and control applications. This paper explores new frameworks for generating learning rules for iteratively computing the principal and minor components (or subspaces) of a given matrix. Stability analysis using Liapunov theory and La Salle invariance principle is provided to determine regions of attraction of these learning rules. Among many derivations, it is specifically shown that Oja's rule and many variations of it are asymptotically globally stable. Liapunov stability theory is also applied to weighted learning rules. Some of the essential features for the proposed MCA/PCA learning rules are that they are self normalized and can be applied to non-symmetric matrices. Exact solutions for some nonlinear dynamical systems are also provided.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1424402107, 9781424402106
StatePublished - 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006Jun 16 2006

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2006 American Control Conference
Country/TerritoryUnited States
CityMinneapolis, MN


  • Analytic solutions
  • Asymptotic stability
  • Dynamical flow
  • Exact solutions
  • Global stability
  • Gradient flow
  • MCA
  • MSA
  • Oja's rule
  • Optimization over stiefel manifold
  • PCA
  • PSA


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