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

1 March 1994

journal article
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 26 (1) , 80-103
https://doi.org/10.2307/1427581

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

This publication has 3 references indexed in Scilit:

Self-organization and a.s. convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli
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Stochastic Approximation Methods for Constrained and Unconstrained Systems
Published by Springer Nature ,1978