Hyperparameter Selection for Self-Organizing Maps

Akio Utsugi

Neural Computation vol. 9, no. 3, pp. 623-635


The self-organizing map (SOM) algorithm for finite data is derived as an approximate MAP estimation algorithm for a Gaussian mixture model with a Gaussian smoothing prior, which is equivalent to a generalized deformable model (GDM). For this model, objective criteria for selecting hyperparameters are obtained on the basis of empirical Bayesian estimation and cross-validation, which are representative model selection methods. The properties of these criteria are compared by simulation experiments. These experiments show that the cross-validation methods favor more complex structures than the expected log likelihood supports, which is a measure of compatibility between a model and data distribution. On the other hand, the empirical Bayesian methods have the opposite bias.

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