GTM: the generative topographic mapping

Christopher M. Bishop, Markus Svensén, Christopher K. I. Williams

    Research output: Working paperTechnical report

    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 transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline.
    Original languageEnglish
    Place of PublicationBirmingham
    PublisherAston University
    Number of pages16
    ISBN (Print)NCRG/96/015
    Publication statusPublished - 1 Jan 1998

    Keywords

    • Latent variable models
    • probability density
    • variables
    • linear transformations
    • latent space
    • data space
    • non-linear
    • generative topographic mapping
    • EM algorithm
    • elf-Organizing Map

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  • Research Output

    GTM: the generative topographic mapping

    Bishop, C. M., Svensén, M. & Williams, C. K. I., 1 Jan 1998, In : Neural Computation. 10, 1, p. 215-235 21 p.

    Research output: Contribution to journalArticle

  • Cite this

    Bishop, C. M., Svensén, M., & Williams, C. K. I. (1998). GTM: the generative topographic mapping. Aston University.