Self-organization and convergence of the one-dimensional Kohonen algorithm

摘要

Here the self-organization and a.s. convergence of one-dimensional Kohonen's algorithm in its 2k-neighbor setting with general type of stimuli distribution and non-increasing learning rate is considered.We show that the probability of self-organization for all initial values of neurons is uniformly positive. Moreover, in the convergence phase the asymptotic behavior of the algorithm is governed by a cooperative and irreducible differential equation. This implies the a.s. convergence of algorithm if the differential equation has a unique fixed point.