Magnification factors for the SOM and GTM algorithms

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

    Research output: Contribution to conferencePaper

    Abstract

    Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.
    Original languageEnglish
    Publication statusPublished - 1997
    EventProceedings 1997 Workshop on Self-Organizing Maps - Helsinki University of Technology, Finland
    Duration: 4 Jun 19976 Jun 1997

    Workshop

    WorkshopProceedings 1997 Workshop on Self-Organizing Maps
    CountryFinland
    CityHelsinki University of Technology
    Period4/06/976/06/97

    Keywords

    • Magnification factors
    • topographic mapping
    • discrete
    • neuro-biological
    • Generative Topographic Mapping
    • differential geometry
    • morphological

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