GTM: A principled alternative to the self-organizing map

Christopher M. Bishop, M. Svens'en, Christopher K. I. Williams, C. von der Malsburg, W. von Selen, J. C. Vorbruggen, B. Sendhoff

    Research output: Working paperTechnical report

    Abstract

    The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general non-linear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multi-phase oil pipeline.
    Original languageEnglish
    Place of PublicationBirmingham
    PublisherAston University
    Number of pages6
    ISBN (Print)NCRG/96/031
    Publication statusPublished - 15 Apr 1997

    Keywords

    • self-organizing map
    • algorithm
    • heuristic ideas
    • density of data
    • latent variable model
    • Generative Topographic Mapping
    • non-linear transformations
    • latent space
    • data space
    • expectation-maximization

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  • Cite this

    Bishop, C. M., Svens'en, M., Williams, C. K. I., von der Malsburg, C., von Selen, W., Vorbruggen, J. C., & Sendhoff, B. (1997). GTM: A principled alternative to the self-organizing map. Aston University.