About the Kohonen algorithm: strong or weak self-organization?

Abstract The question of self-organization for the Kohonen algorithm is investigated. First the notions of organized states, weak and strong self-organizations are precisely defined. Then, combining mathematical and simulation results we prove that the Kohonen algorithm has not the strong self-organization property at least in two well-known cases: the stimuli space is [0, 1]2, the unit set is a line (resp. a grid) with the two nearest (resp. eight nearest) neighbourhood function. Copyright © 1996 Elsevier Science Ltd