Learning and forgetting - how they should be balanced in SOM algorithm

A two layered neural network is considered as Kohonen´s dot-product type SOM model. It defines pattern classifiers through step by step self-organization. This note examines the role of learning rate α and forgetting rate δ in such SOM algorithms. The properties we consider are the relation between stability of winner functions and topographic mapping formation. We propose three classes of networks defining corresponding winner functions. They depend on the two parameters or their ratio K, and the former class includes the latter and the most restrictive class is here called K-topographic. The main result is 1) we can define such topographic networks depending on the ratio K and 2) once a network belongs to this K-topographic class we can maintain the property in the evolution process if we choose α and δ appropriately. Thus the stability and topographic property are related in this generalized SOM algorithm.