Regularized SOM-training: a solution to the topology-approximation dilemma?

The self-organizing map (SOM) is a tool which combines the task of vector quantisation with a topologically ordered representation of the training vectors. The topological order is obtained by an adaptation of the winner and its neighbours towards the input vector and leads to several effects, which reduce the approximation quality. Topology and approximation seem to be contradictory. This is linked to the training properties and not to the data set. It may be reduced by a modification of the training towards a better regularity of the generated map. This new principle is proposed in this paper and may replace the neighbourhood adaptation in the final phase of the training. This paper presents examples of the standard SOM-training and regularized training and visualizes the topology-approximation dilemma graphically with two different data sets