title: SOM's mathematics.
abstract: 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 various questions.
authors.affiliation: Laboratoire de Statistique et Probabilités, 118 route de Narbonne, Toulouse, France. fort@math.ups-tlse.fr
authors.forename: J C
authors.initials: JC
authors.lastname: Fort
mesh_terms: D017709:Fractals; D008433:Mathematics; D008962:Models, Theoretical