Convergence in Distribution of the One-Dimensional Kohonen Algorithms when the Stimuli are not Uniform
Catherine Bouton, Gilles Pagès · Advances in Applied Probability · 1994
We show that the one-dimensional self-organizing Kohonen algorithm (with zero or two neighbours and constant step ε ) is a Doeblin recurrent Markov chain provided that the stimuli distribution μ is lower bounded by the Lebesgue measure on some open set. Some properties of the invariant probability measure v ε (support, absolute continuity, etc.) are established as well as its asymptotic behaviour as ε ↓ 0 and its robustness with respect to μ.