Generalizations of Oja´s Learning Rule to Non-Symmetric Matrices

Author

Hasan, Mohammed A.

Author_Institution

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

fYear

2007

fDate

27-30 May 2007

Firstpage

1779

Lastpage

1782

Abstract

New learning rules for computing eigenspaces and eigenvectors for symmetric and nonsymmetric matrices are proposed. By applying Liapunov stability theory, these systems are shown to be globally convergent. Properties of limiting solutions of the systems and weighted versions are also examined. The proposed systems may be viewed as generalizations of Oja´s and Xu´s principal subspace learning rules. Numerical examples showing the convergence behavior are also presented.

Keywords

eigenvalues and eigenfunctions; learning (artificial intelligence); numerical stability; principal component analysis; Liapunov stability theory; Oja learning rule; convergence behavior; eigenspaces computing; eigenvectors computing; global convergence; limiting solutions; minor components; nonsymmetric matrices; principal components; principal subspace learning rules; symmetric matrices; weighted versions; Convergence of numerical methods; Eigenvalues and eigenfunctions; Lagrangian functions; Lyapunov method; Principal component analysis; Signal analysis; Signal processing; Signal processing algorithms; Stability; Symmetric matrices; Liapunov stability; Oja´s learning rule; global convergence; minor components; principal components;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2007. ISCAS 2007. IEEE International Symposium on

Conference_Location

New Orleans, LA

Print_ISBN

1-4244-0920-9

Electronic_ISBN

1-4244-0921-7

Type

conf

DOI

10.1109/ISCAS.2007.378017

Filename

4253004