Analysis of SOM-Based Models for the Development of Visual Maps

H.-U. Bauer, MPI Str"omungsforschung, Postfach 28 53, 37018 G\"ottingen, Germany,
M. Riesenhuber, Center for Biol. and Comp. Learning MIT E25-221, Cambridge, MA 02139, USA,
D. Brockmann, MPI Str"omungsforschung, Postfach 28 53, 37018 G\"ottingen, Germany,
T. Geisel, MPI Str"omungsforschung, Postfach 28 53, 37018 G\"ottingen, Germany
Email: dbrockm1@gwdg.de

Abstract:

The high-dimensional version of Kohonen's SOM-algorithm is the basis of several models for the development of topographic maps in the brain, in particular of ocular dominance and orientation maps in the visual cortex. We describe here a mathematical technique to analyze the pattern formation behaviour of such models. The method is based on an evaluation of a distortion function for several possible stimulus space tesselations which correspond to different states of the map. As an illustration of the method we analyze a high-dimensional SOM-model for the development of ocular dominance maps.

WSOM'97