Magnification factors for the GTM algorithm

Christopher M. Bishop, Markus Svens'en, Christopher K. I. Williams

    Research output: Chapter in Book/Published conference outputChapter


    The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.
    Original languageEnglish
    Title of host publicationFifth International Conference on Artificial Neural Networks
    Place of PublicationCambridge, UK
    Number of pages6
    ISBN (Print)0852966903
    Publication statusPublished - 9 Jul 1997
    EventProceedings IEE Fifth International Conference on Artificial Neural Networks -
    Duration: 9 Jul 19979 Jul 1997


    ConferenceProceedings IEE Fifth International Conference on Artificial Neural Networks

    Bibliographical note

    Conference Publication No 440 ©1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.


    • Generative Topographic Mapping
    • Self-organizing map
    • reference vectors
    • continuous mapping
    • morphological data


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