Kohonen neural networks and genetic classification

TL;DR

This paper analyzes the convergence properties of Kohonen neural networks, providing rigorous conditions for almost everywhere convergence, and applies these findings to genetic classification, a rapidly growing application area.

Contribution

It offers a rigorous proof of convergence conditions for the Kohonen algorithm and connects these conditions to practical learning parameter choices, with applications to genetic classification.

Findings

Most used decay rate of learning parameter ensures convergence

Provided rigorous proof of a.e. convergence under certain conditions

Applied convergence analysis to genetic classification

Abstract

We discuss the property of a.e. and in mean convergence of the Kohonen algorithm considered as a stochastic process. The various conditions ensuring the a.e. convergence are described and the connection with the rate decay of the learning parameter is analyzed. The rate of convergence is discussed for different choices of learning parameters. We proof rigorously that the rate of decay of the learning parameter which is most used in the applications is a sufficient condition for a.e. convergence and we check it numerically. The aim of the paper is also to clarify the state of the art on the convergence property of the algorithm in view of the growing number of applications of the Kohonen neural networks. We apply our theorem and considerations to the case of genetic classification which is a rapidly developing field.