Self Organizing Map algorithm and distortion measure

Details Self Organizing Map algorithm and distortion measure Self Organizing Map algorithm and distortion measure

2008-02-21

arxiv.org/abs/0802.3150v1

Neural Networks 19, 6-7 (2006) 671-678

Statistics

Machine Learning

Scientific paper

We study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of distortion measure. If we assume that the observations and the map lie in an compact Euclidean space, we prove the strong consistency of the map which almost minimizes the empirical distortion. Moreover, after calculating the derivatives of the theoretical distortion measure, we show that the points minimizing this measure and the equilibria of the Kohonen map do not match in general. We illustrate, with a simple example, how this occurs.

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