  This work presents a mathematical treatment of the relation between
Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that
energy-based SOM models can be interpreted as performing gradient descent,
minimizing an approximation to the GMM log-likelihood that is particularly
valid for high data dimensionalities. The SOM-like decrease of the neighborhood
radius can be understood as an annealing procedure ensuring that gradient
descent does not get stuck in undesirable local minima. This link allows to
treat SOMs as generative probabilistic models, giving a formal justification
for using SOMs, e.g., to detect outliers, or for sampling.
