A Bayesian analysis of self-organizing maps

  • Authors:
  • Stephen P. Luttrell

  • Affiliations:
  • -

  • Venue:
  • Neural Computation
  • Year:
  • 1994

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Abstract

In this paper Bayesian methods are used to analyze some of theproperties of a special type of Markov chain. The forwardtransitions through the chain are followed by inverse transitions(using Bayes' theorem) backward through a copy of the same chain;this will be called a folded Markov chain. If an appropriatelydefined Euclidean error (between the original input and its"reconstruction" via Bayes' theorem) is minimized with respect tothe choice of Markov chain transition probabilities, then thefamiliar theories of both vector quantizers and self-organizingmaps emerge. This approach is also used to derive the theory ofself-supervision, in which the higher layers of a multilayernetwork supervise the lower layers, even though overall there is noexternal teacher.