Convergence properties of a class of learning vector quantization algorithms

Author

Kosmatopoulos, Elias B. ; Christodoulou, Manolis A.

Author_Institution

Dept. of Electron. & Comput. Eng., Tech. Univ. of Crete, Chania, Greece

Volume

5

Issue

2

fYear

1996

fDate

2/1/1996 12:00:00 AM

Firstpage

361

Lastpage

368

Abstract

A mathematical analysis of a class of learning vector quantization (LVQ) algorithms is presented. Using an appropriate time-coordinate transformation, we show that the LVQ algorithms under consideration can be transformed into linear time-varying stochastic difference equations. Using this fact, we apply stochastic Lyapunov stability arguments, and we prove that the LVQ algorithms under consideration do indeed converge, provided that some appropriate conditions hold

Keywords

Lyapunov methods; adaptive signal processing; convergence of numerical methods; difference equations; learning (artificial intelligence); stochastic processes; vector quantisation; LVQ algorithms; adaptive signal processing; convergence properties; learning vector quantization algorithms; linear time-varying stochastic difference equations; mathematical analysis; stochastic Lyapunov stability; time coordinate transformation; Convergence; Data compression; Drives; Neural networks; Partitioning algorithms; Probability distribution; Senior members; Signal processing algorithms; Stochastic processes; Vector quantization;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.480771

Filename

480771