Convergence in Distribution of the One-Dimensional Kohonen Algorithms when the Stimuli are not Uniform

1 March 1994

journal article
general applied-probability
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 26 (01) , 80-103
https://doi.org/10.1017/s0001867800026021

Abstract

We show that the one-dimensional self-organizing Kohonen algorithm (with zero or two neighbours and constant step ε) is a Doeblin recurrent Markov chain provided that the stimuli distribution μ is lower bounded by the Lebesgue measure on some open set. Some properties of the invariant probability measure v^ε (support, absolute continuity, etc.) are established as well as its asymptotic behaviour as ε ↓ 0 and its robustness with respect to μ.

Keywords

MARKOV CHAINS
DOEBLIN RECURRENCE
NEURAL NETWORKS
60J20
60F99

This publication has 1 reference indexed in Scilit:

Analysis of a simple self-organizing process
Biological Cybernetics, 1982