Metrics and the Cooperative Process of the Self-organizing Map Algorithm

This paper explores effects of using different the distance measures in the cooperative process of the Self-Organizing Map algorithm on the resulting map. In standard implementations of the algorithm, Euclidean distance is normally used. However, experimentation with non-Euclidean metrics shows that this is not the only metric that works. For example, versions of the SOM algorithm using the Manhattan metric, and metrics in the same family as the Euclidean metric, can converge, producing sets of weight vectors indistinguishable from the regular SOM algorithm. However, just being a metric is not enough: two examples of such are described. Being analogous to the Euclidean metric is not enough either, and we exhibit members of a family of such distance measures that do not produce satisfactory maps.