Asymptotic level density for a class of vector quantization processes

  • Authors:
  • H. Ritter

  • Affiliations:
  • Dept. of Phys., Illinois Univ., Urbana, IL

  • Venue:
  • IEEE Transactions on Neural Networks
  • Year:
  • 1991

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Abstract

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)α , where the exponent α depends on the number n of neighbors on each side of a unit and is given by α=2/3-1/(3n 2+3[n+1]2). The asymptotic level density is calculated, and Monte Carlo simulations are presented