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.