Magnification factors for the GTM algorithm


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.

Divisions: Aston University (General)
Additional Information: 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.
Event Title: Proceedings IEE Fifth International Conference on Artificial Neural Networks
Event Type: Other
Event Dates: 1997-07-09 - 1997-07-09
Uncontrolled Keywords: Generative Topographic Mapping,Self-organizing map,reference vectors,continuous mapping,morphological data
ISBN: 0852966903
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Publisher URL)
http://ieeexplo ... ber=13303?tag=1 (Publisher URL)
PURE Output Type: Chapter
Published Date: 1997-07-09
Authors: Bishop, Christopher M.
Svens'en, Markus
Williams, Christopher K. I.



Version: Published Version

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