GTM: A principled alternative to the self-organizing map

Abstract

The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general non-linear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multi-phase oil pipeline.

Divisions: Aston University (General)
Uncontrolled Keywords: self-organizing map,algorithm,heuristic ideas,density of data,latent variable model,Generative Topographic Mapping,non-linear transformations,latent space,data space,expectation-maximization
ISBN: NCRG/96/031
PURE Output Type: Technical report
Published Date: 1997-04-15
Authors: Bishop, Christopher M.
Svens'en, M.
Williams, Christopher K. I.
von der Malsburg, C.
von Selen, W.
Vorbruggen, J. C.
Sendhoff, B.

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