SELF-ORGANIZATION AND AS CONVERGENCE OF THE ONE-DIMENSIONAL KOHONEN ALGORITHM WITH NONUNIFORMLY DISTRIBUTED STIMULI

This paper shows that the 2-neighbour Kohonen algorithm is self-organi zing under pretty general assumptions on the stimuli distribution mu ( supp(mu(c)) contains a non-empty open set) and is a.s. convergent-in a weakened sense-as soon as mu admits a log-concave density. The 0-neig hbour algorithm is shown to have similar converging properties. Some n umerical simulations illustrate the theoretical results and a counter- example provided by a specific class of density functions.