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

    Fingerprint

    topographic mapping
    oil pipeline
    factor analysis

    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. Birmingham: Aston University.
    Bishop, Christopher M. ; Svensén, Markus ; Williams, Christopher K. I. / GTM: the generative topographic mapping. Birmingham : Aston University, 1998.
    @techreport{fedfcd103bbe49888782f8e55f6e5827,
    title = "GTM: the generative topographic mapping",
    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.",
    keywords = "Latent variable models, probability density, variables, linear transformations, latent space, data space, non-linear, generative topographic mapping, EM algorithm, elf-Organizing Map",
    author = "Bishop, {Christopher M.} and Markus Svens{\'e}n and Williams, {Christopher K. I.}",
    year = "1998",
    month = "1",
    day = "1",
    language = "English",
    isbn = "NCRG/96/015",
    publisher = "Aston University",
    type = "WorkingPaper",
    institution = "Aston University",

    }

    Bishop, CM, Svensén, M & Williams, CKI 1998 'GTM: the generative topographic mapping' Aston University, Birmingham.

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

    Birmingham : Aston University, 1998.

    Research output: Working paperTechnical report

    TY - UNPB

    T1 - GTM: the generative topographic mapping

    AU - Bishop, Christopher M.

    AU - Svensén, Markus

    AU - Williams, Christopher K. I.

    PY - 1998/1/1

    Y1 - 1998/1/1

    N2 - 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.

    AB - 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.

    KW - Latent variable models

    KW - probability density

    KW - variables

    KW - linear transformations

    KW - latent space

    KW - data space

    KW - non-linear

    KW - generative topographic mapping

    KW - EM algorithm

    KW - elf-Organizing Map

    M3 - Technical report

    SN - NCRG/96/015

    BT - GTM: the generative topographic mapping

    PB - Aston University

    CY - Birmingham

    ER -

    Bishop CM, Svensén M, Williams CKI. GTM: the generative topographic mapping. Birmingham: Aston University. 1998 Jan 1.