Reduced risk of Kohonen´s feature map non-convergence by an individual size of the neighborhood

Kohonen´s (1984) self-organized feature map is an effective neural network for unsupervised vector quantization and topology-preserving mapping. It is admitted that this network might get stuck in a local minimum. An empirical analysis of the learning dynamics shows two purposes for weight adaptation: the updating either modifies the global arrangement of the cells or refines the local topological mapping. We propose a new evaluation of the neighborhood size as a function of the distance between the input pattern and the weight vector of the winning neuron. The new algorithm provides a smooth transition. An application of this approach for a benchmark problem is described and its performance is compared to that of the standard algorithm. A qualitative analysis is given in order to bring out the ability of the network to cope with fast neighborhood-size reduction