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: , 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.

Tue May 27 12:40:37 EET DST 1997