Diffusion approximation of frequency sensitive competitive learning

Author

Galanopoulos, Aristides S. ; Moses, Randolph L. ; Ahalt, Stanley C.

Author_Institution

Dept. of Electr. Eng., Ohio State Univ., Columbus, OH, USA

Volume

8

Issue

5

fYear

1997

fDate

9/1/1997 12:00:00 AM

Firstpage

1026

Lastpage

1030

Abstract

The focus of this paper is a convergence study of the frequency sensitive competitive learning (FSCL) algorithm. We approximate the final phase of FSCL learning by a diffusion process described by the Fokker-Plank equation. Sufficient and necessary conditions are presented for the convergence of the diffusion process to a local equilibrium. The analysis parallels that by Ritter-Schulten (1988) for Kohonen´s self-organizing map. We show that the convergence conditions involve only the learning rate and that they are the same as the conditions for weak convergence described previously. Our analysis thus broadens the class of algorithms that have been shown to have these types of convergence characteristics

Keywords

approximation theory; convergence of numerical methods; diffusion; learning systems; probability; self-organising feature maps; unsupervised learning; vector quantisation; Fokker-Plank equation; convergence; diffusion approximation; frequency sensitive competitive learning; learning systems; necessary condition; probability; self-organizing map; sufficient condition; vector quantisation; Algorithm design and analysis; Convergence; Diffusion processes; Equations; Frequency; Learning systems; Neural networks; Power capacitors; Stochastic processes; Vector quantization;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.623204

Filename

623204