Analysis of Dynamical Systems for Generalized Principal and Minor Component Extraction

Author

Hasan, Mohammed A.

Author_Institution

Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN

fYear

2006

fDate

12-14 July 2006

Firstpage

531

Lastpage

535

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

Keywords

eigenvalues and eigenfunctions; feature extraction; gradient methods; principal component analysis; stability; dynamical systems; eigenvalue problem; generalized principal; global stability; gradient-like systems; minor component extraction; principal component analysis; Algorithm design and analysis; Asymptotic stability; Convergence; Eigenvalues and eigenfunctions; Linear discriminant analysis; Nonlinear dynamical systems; Principal component analysis; Stability analysis; Standards development; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Sensor Array and Multichannel Processing, 2006. Fourth IEEE Workshop on

Conference_Location

Waltham, MA

Print_ISBN

1-4244-0308-1

Type

conf

DOI

10.1109/SAM.2006.1706190

Filename

1706190