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Overtraining and model selection with the self-organizing map

We discuss the importance of finding the correct model complexity and regularization level, in the self-organizing map (SOM) algorithm. The complexity of the SOM is determined mainly by the width of the final neighborhood, which is usually chosen ad hoc or set to zero for optimal quantization error. However, if the SOM is used for visualizing the joint probability distribution of the data, then care must be taken not to overfit the model to the data sample, similarly as with any statistical model. We propose a heuristic criterion for model selection in SOM, and demonstrate by simulations that the criterion can be used for selecting the neighborhood that suppresses overfitting.