GTM: the generative topographic mapping

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

    Research output: Contribution to journalArticle

    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
    Pages (from-to)215-235
    Number of pages21
    JournalNeural Computation
    Volume10
    Issue number1
    Publication statusPublished - 1 Jan 1998

    Fingerprint

    Play and Playthings
    Statistical Factor Analysis
    Oils
    Generative
    Self-organizing Map
    Toys
    Oil
    Diagnostics
    Factor Analysis
    Hidden Variables

    Keywords

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

    Cite this

    Bishop, C. M., Svensén, M., & Williams, C. K. I. (1998). GTM: the generative topographic mapping. Neural Computation, 10(1), 215-235.
    Bishop, Christopher M. ; Svensén, Markus ; Williams, Christopher K. I. / GTM: the generative topographic mapping. In: Neural Computation. 1998 ; Vol. 10, No. 1. pp. 215-235.
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    Bishop, CM, Svensén, M & Williams, CKI 1998, 'GTM: the generative topographic mapping', Neural Computation, vol. 10, no. 1, pp. 215-235.

    GTM: the generative topographic mapping. / Bishop, Christopher M.; Svensén, Markus; Williams, Christopher K. I.

    In: Neural Computation, Vol. 10, No. 1, 01.01.1998, p. 215-235.

    Research output: Contribution to journalArticle

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    Bishop CM, Svensén M, Williams CKI. GTM: the generative topographic mapping. Neural Computation. 1998 Jan 1;10(1):215-235.