Constrained clustering and Kohonen self-organizing maps

The Self-Organizing Feature Maps (SOFM; Kohonen 1984) algorithm is a well-known example of unsupervised learning in connectionism and is a clustering method closely related to the k-means. Generally the data set is available before running the algorithm and the clustering problem can be approached by an inertia criterion optimization. In this paper we consider the probabilistic approach to this problem. We propose a new algorithm based on the Expectation Maximization principle (EM; Dempster, Laird, and Rubin 1977). The new method can be viewed as a Kohonen type of EM and gives a better insight into the SOFM according to constrained clustering. We perform numerical experiments and compare our results with the standard Kohonen approach.