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

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    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

    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. Birmingham: Aston University.
    Bishop, Christopher M. ; Svens'en, M. ; Williams, Christopher K. I. ; von der Malsburg, C. ; von Selen, W. ; Vorbruggen, J. C. ; Sendhoff, B. / GTM: A principled alternative to the self-organizing map. Birmingham : Aston University, 1997.
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    title = "GTM: A principled alternative to the self-organizing map",
    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.",
    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",
    author = "Bishop, {Christopher M.} and M. Svens'en and Williams, {Christopher K. I.} and {von der Malsburg}, C. and {von Selen}, W. and Vorbruggen, {J. C.} and B. Sendhoff",
    year = "1997",
    month = "4",
    day = "15",
    language = "English",
    isbn = "NCRG/96/031",
    publisher = "Aston University",
    type = "WorkingPaper",
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    Bishop, CM, Svens'en, M, Williams, CKI, von der Malsburg, C, von Selen, W, Vorbruggen, JC & Sendhoff, B 1997 'GTM: A principled alternative to the self-organizing map' Aston University, Birmingham.

    GTM: A principled alternative to the self-organizing map. / Bishop, Christopher M.; Svens'en, M.; Williams, Christopher K. I.; von der Malsburg, C.; von Selen, W.; Vorbruggen, J. C.; Sendhoff, B.

    Birmingham : Aston University, 1997.

    Research output: Working paperTechnical report

    TY - UNPB

    T1 - GTM: A principled alternative to the self-organizing map

    AU - Bishop, Christopher M.

    AU - Svens'en, M.

    AU - Williams, Christopher K. I.

    AU - von der Malsburg, C.

    AU - von Selen, W.

    AU - Vorbruggen, J. C.

    AU - Sendhoff, B.

    PY - 1997/4/15

    Y1 - 1997/4/15

    N2 - 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.

    AB - 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.

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    KW - algorithm

    KW - heuristic ideas

    KW - density of data

    KW - latent variable model

    KW - Generative Topographic Mapping

    KW - non-linear transformations

    KW - latent space

    KW - data space

    KW - expectation-maximization

    M3 - Technical report

    SN - NCRG/96/031

    BT - GTM: A principled alternative to the self-organizing map

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    Bishop CM, Svens'en M, Williams CKI, von der Malsburg C, von Selen W, Vorbruggen JC et al. GTM: A principled alternative to the self-organizing map. Birmingham: Aston University. 1997 Apr 15.