Self-organization using Potts models

-In this work, we use Potts neurons for the competitive mechanism in a self-organization model. We obtain new algorithms on the basis of a Potts neural network for coherent mapping, and we remodel the Durbin algorithm and the Kohonen algorithm with mean field annealing. The resulting dimension-reducing mappings possess a highly reliable topology preservation such that the nearby elements in the parameter space are ordered as similarly as possible on the cortex-like map, and the objective function costs between neighboring cortical points are as smooth as possible. The proposed Potts neural network contains two sets of interactive dynamics for two kinds of mappings, one from the parameter space to the cortical space and the other in the reverse way. We present a theoretical approach to developing self-organizing algorithms with a novel decision principle for competitive learning. We find that one Ports neuron is able to implement the Kohonen algorithm. Both implementation and simulation results are encouraging. Copyright ©1996 Elsevier Science Lid Keywords---Self-organization map, Neural network, Potts model, Elastic ring, Mean field annealing, Hairy model.