Self-organization of orientation maps in a formal neuron model using a cluster learning rule

Self-organization of orientation maps due to external stimuli in the primary visual area of the cerebral cortex is studied in a two-layered neural network which consists of formal neuron models with a sigmoidal output function. A cluster learning rule is proposed as an extended Hebbian learning rule, where a modification of synaptic connections is influenced by an activation of neighboring output neurons. By making use of self-consistent Monte Carlo method, we evaluate output responses of neurons against explicit inputs after the learning. An orientation map calculated from the output responses reproduces characteristic features of biological ones. Moreover quantitative analysis of our results are consistent with those of experimental results. It is shown that the cluster learning rule plays an important role in forming smooth changes of preferred orientations.