ASYMPTOTIC LEVEL DENSITY FOR A CLASS OF VECTOR QUANTIZATION PROCESSES

We show 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)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/(3n2 + 3[n + 1]2).