Code Vector Density in Topographic Mappings

Abstract

In this memorandum we present an informally argued derivation of the properties of topographic vector quantisers in the limit of a large codebook size. In particular, we prove that the code vector density does not depend on one's choice of neighbourhood function, provided that we use the minimum distortion (rather than the nearest neighbour) encoding prescription. This result suggests that widespread use of the nearest neighbour prescription in topographic mapping networks is fundamentally misguided. It would be advisable to remember that the nearest neighbour prescription is assumed not derived, so its adherents must accept defeat gracefully.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1992
Accession Number
ADA258222

Entities

People

  • Stephen P. Lutrell

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Coding
  • Copyrights
  • Covariance
  • Curvature
  • Decoding
  • Distortion
  • Equations
  • Image Processing
  • Integrals
  • Lyapunov Functions
  • Markov Chains
  • Notation
  • Probability
  • Standards
  • Stationary
  • Translations

Readers

  • Mathematical Modeling and Probability Theory.
  • Neural Network Machine Learning.
  • Strategic Security Studies