PHASE-DIAGRAMS OF SELF-ORGANIZING MAPS

We present a method which allows the analytic determination of phase d iagrams in the self-organizing map, a model for the formation of topog raphic projection patterns in the brain and in signal processing appli cations. The method only requires an ansatz for the tesselation of the data space induced by the map, not for the explicit state of the map. We analytically obtain phase diagrams for various examples, including models for the development of orientation and ocular-dominance maps. The latter phase diagram exhibits transitions to broadening ocular-dom inance patterns as observed in a recent experiment.