GTM: The Generative Topographic Mapping

Abstract

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis, which is based on a linear transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm. GTM provides a principled alternative to the widely used self-organizing map (SOM) of Kohonen (1982) and overcomes most of the signicant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from ow diagnostics for a mul-tiphase oil pipeline.

DOI: 10.1162/089976698300017953

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Showing 1-10 of 22 references

Neural networks for pattern recognition

  • C M Bishop
  • 1995
Highly Influential
5 Excerpts

A fast EM algorithm for latent variable density models

  • C M Bishop, M Svensén, C K I Williams
  • 1996
Highly Influential
1 Excerpt

On estimating regression. Theory of Probability and Its Applications

  • E A Nadaraya
  • 1964
Highly Influential
1 Excerpt

Using self-organizin g maps to classify radar range proles

  • S P Luttrell
  • 1995
1 Excerpt

Adaptive principal surfaces

  • M Leblanc, R Tibshirani
  • 1994
1 Excerpt
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