Analyzing the formation of structure in high-dimensional Self-Organizing Maps reveals differences to feature map models

Abstract

We present a method for calculating phase diagrams for the high-dimensional variant of the Self-Organizing Map (SOM). The method requires only an ansatz for the tesselation of the data space induced by the map, not for the explicit state of the map. Using this method we analyze two recently proposed models for the development of orientation and ocular dominance column maps. The phase transition condition for the orientation map turns out to be of different form than of the corresponding low-dimensional map.