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SOM algorithms and their stability consideration

A two layered feedforward neural network is considered as Kohonen’s dot-product type SOM model which defines a winner function f from an input pattern set into an output unit set. It defines pattern classifiers through step by step self-organization. What kinds of classifiers they can ultimately be and how they are attained asymptotically are the basic problems to be solved. Our main result is that the property of being topographic can be preserved by appropriately choosing learning rates and hence the winner function becomes stable in this case.