Interactive statistical experiments with template-matching neural networks

Abstract

A personal computer with a novel interactive simulation program is used to study competitive learning (Kohonen learning) in neural networks with random input patterns. Specifically, it is shown how such networks can be used for statistical measurements. Little mathematical analysis of this problem appears to exist, but Kohonen proposed that the learned-template output of a competitive network reflects statistical properties of the input-pattern distribution. The simulation experiments bear out this conjecture. As learning proceeds the n learned templates become approximately equiprobable; the author also measures an estimate of the learned-output entropy, which correctly increases to an accurate approximation of log2(n) bits. For two-dimensional pattern vectors, it is possible to display animated random walks of the output templates converging to produce vector quantization of the pattern space.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>