# Hyperparameter Selection for Self-Organizing Maps

Akio Utsugi

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

### Abstract:

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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