About the convergence of the generalized Kohonen algorithm
The Kohonen algorithm was originally devised and studied by Kohonen in 1982 (see , ). Unfortunately, as far as mathematical treatment is concerned, rigourous results are not so easy to establish. For instance, any simulation in a one dimensional setting (i.e. with scalar inputs) shows the existence of a self-organization property. Nevertheless, the proof of such a property requires some non trivial Markov material. It was first carried out in  for uniformly distributed stimuli and then was extended to general distributions in . Many open questions related to the one dimensional self-organization still remain, and no similar result was proved in higher dimension so far.
KeywordsEquilibrium Point Weight Vector Stochastic Approximation Borel Probability Measure Neighbourhood Function
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