Topology selection for self-organizing maps

A topology-selection method for self-organizing maps (SOMs) based on empirical Bayesian inference is presented. This method is a natural extension of the hyperparameter-selection method presented earlier, in which the SOM algorithm is regarded as an estimation algorithm for a Gaussian mixture model with a Gaussian smoothing prior on the centroid parameters, and optimal hyperparameters are obtained by maximizing their evidence. In the present paper, comparisons between models with different topologies are made possible by further specifying the prior of the centroid parameters with an additional hyperparameter. In addition, a fast hyperparameter-search algorithm using the derivatives of evidence is presented. The validity of the methods presented is confirmed by simulation experiments.