Density Estimation by Mixture Models with Smoothing Priors

In the statistical approach for self-organizing maps (SOMs), learning is regarded as an estimation algorithm for a gaussian mixture model with a gaussian smoothing prior on the centroid parameters. The values of the hyperparameters and the topological structure are selected on the basis of a statistical principle. However, since the component selection probabilities are fixed to a common value, the centroids concentrate on areas with high data density. This deforms a coordinate system on an extracted manifold and makes smoothness evaluation for the manifold inaccurate. In this article, we study an extended SOM model whose component selection probabilities are variable. To stabilize the estimation, a smoothing prior on the component selection probabilities is introduced. An estimation algorithm for the parameters and the hyperparameters based on empirical Bayesian inference is obtained. The performance of density estimation by the new model and the SOM model is compared via simulation experiments.