Stability of Self-Organizing Processes

Abstract

This paper treats the stability of the Markov chain involved in the self-organizing feature maps of Kohonen. These maps have values that give an empirical approximation to a probability distribution while at the same time attempting to preserve a neighborhood topology. Some of the processes have the property that two initial states subjected to the same dynamics approach each other exponentially fast with probability one. This in turn implies a strong form of stability. Thus the initial state or the process is merely a transient effect. The environment alone determines future history.