Kohonen Self-Organizing Maps: Is the Normalization Necessary?
Pierre Demartines
Current address: Laboratoire de Traitement d'Images et de Reconnaissance des Formes, Institut National Polytechnique de Grenoble,
46 av. Felix-Viallet, F-38031 Grenoble, France
Francois Blayo
Laboratoire de Microinformatique, Ecole Polytechnique Federale de Lausanne,
INF-Ecublens, CH-1015 Lausanne, Switzerland
Abstract
The self-organizing algorithm of Kohonen is well known for its ability to map an input space with a neural network. According to multiple observations, self organization seems to be an essential feature of the brain. In this paper we focus on the distance measure used by the neurons to determine which one is closest to an input stimulus. The distance measures proposed until now are not very satisfactory, from either a biological or computational point of view. Using mathematical considerations and numerical simulations, we show that the original dot product measure is applicable without input normalization when the dimension of the input space is high. When adding a feature of biological neurons (accommodation) to the algorithm, the network converges with normalization as well (in our simulations, for a dimension 
).
