Mathematical Aspects of the Kohonen algorithm

Marie Cottrell (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique

Since the discovery of the SOM's by T. Kohonen, many results that provide a better description of their behaviour have been found. Most of them are very convincing but from a mathematical point of view, only a few are actually proved. In this paper, we make a review of some results that are still to be proved and give some framework to formulate variousquestions.

Mots clés: Kohonen maps; stochastic processes; self-organizing algorithm; quantization

Domaines: Statistiques [math.ST]; Adaptation et Systèmes auto-organisés [nlin.AO]

Marie Cottrell. Mathematical Aspects of the Kohonen algorithm. 7th International Conference on Operations Research, 2006, The Habana, Cuba. ⟨hal-00113911⟩