Phase diagrams of self-organizing maps

We present a method which allows the analytic determination of phase diagrams in the self-organizing map, a model for the formation of topographic projection patterns in the brain and in signal processing applications. 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-dominance patterns as observed in a recent experiment.