Papers and Java demo available

[Akio Utsugi]

The following preprints can be found in
http://www.aist.go.jp/NIBH/~b0616/research.html


Hyperparameter Selection for Self-Organizing Maps
A. Utsugi
To appear in Neural Computation, vol. 9, no. 2.

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.


Topology Selection for Self-Organizing Maps
A. Utsugi
To appear in Network: Computation in Neural Systems, vol. 7, no. 4.

Abstract: 
A topology-selection method for self-organizing maps (SOMs) based on
empirical Bayesian inference is presented. This method is natural 
extension of the hyperparameter-selection method presented earlier, 
in which the SOM algorithm is regarded as an estimation algorithm
for a Gaussian mixture model with a Gaussian smoothing prior on the 
centroid parameters, and optimal hyperparameters are obtained by 
maximizing their evidence. In the present paper, comparisons between 
models with different topologies are made possible by further 
specifying the prior of the centroid parameters with an additional 
hyperparameter. In addition, a fast hyperparameter-search algorithm
using the derivatives of evidence is presented. The validity of the 
methods presented is confirmed by simulation experiments.


In addition, I made a demonstration program for the above theory
using a Java applet, which is accessible via a WWW-browser.

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Akio Utsugi

National Institute of Bioscience and Human-Technology