Title :
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
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;
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
DOI :
10.1109/ISCAS.2007.378017
