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In the 1-dimensional case the algorithm has been shown to converge almost surely [3]. In the case of a very large number of neurons and final neighborhood radius of R the asymptotic point density of the reference vectors of the SOM has been shown to be proportional to: tex2html_wrap_inline3256 , where p(x) is the density function of the inputs x [36, 37]. When the dimension of the input vectors increases the exponent approaches unity so that the distribution of weight vectors estimates that of the training data.

Juha Vesanto
Tue May 27 12:40:37 EET DST 1997