Magnification factors for the GTM algorithm

Christopher M. Bishop, M. Svensén, C. K. I. Williams

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

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 publicationArtificial Neural Networks, Fifth International Conference on (Conf. Publ. No. 440)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages6
ISBN (Print)0-85296-690-3
Publication statusPublished - 1 Jan 1997


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