GTM: the generative topographic mapping

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

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number1
    Publication statusPublished - 1 Jan 1998


    • 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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    • GTM: the generative topographic mapping

      Bishop, C. M., Svensén, M. & Williams, C. K. I., 1 Jan 1998, Birmingham: Aston University, 16 p.

      Research output: Preprint or Working paperTechnical report

      Open Access

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