Neural Computation vol. 10, no. 8, pp. 2115-2135
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 paper, we study an extended SOM model whose component selection probabilities
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.