Markov random walk representations with continuous distributions

  • Authors:
  • Chen-Hsiang Yeang;Martin Szummer

  • Affiliations:
  • MIT Artificial Intelligence Laboratory, Cambridge, MA;Microsoft Research, Cambridge, U.K.

  • Venue:
  • UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
  • Year:
  • 2002

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Abstract

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the data density. We relate this diffusion equation to a path integral and derive the corresponding path probability measure. The framework is useful for incorporating continuous data densities and prior knowledge.