SOM's mathematics

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. (c) 2006 Elsevier Ltd. All rights reserved.