Asymptotic level density for a class of vector quantization processes

It is shown that for a class of vector quantization processes, related to neural modeling, that the asymptotic density Q(x) of the quantization levels in one dimension in terms of the input signal distribution P(x) is a power law Q(x)=C-P(x)/sup alpha /, where the exponent alpha depends on the number n of neighbors on each side of a unit and is given by alpha =2/3-1/(3n/sup 2/+3(n+1)/sup 2/). The asymptotic level density is calculated, and Monte Carlo simulations are presented.<
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