Developments of the generative topographic mapping

Christopher M. Bishop; Markus Svensén; Christopher K. I. Williams

doi:10.1016/S0925-2312(98)00043-5

Developments of the generative topographic mapping

Christopher M. Bishop^*, Markus Svensén, Christopher K. I. Williams

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The generative topographic mapping (GTM) model was introduced by Bishop et al. (1998, Neural Comput. 10(1), 215-234) as a probabilistic re- formulation of the self-organizing map (SOM). It offers a number of advantages compared with the standard SOM, and has already been used in a variety of applications. In this paper we report on several extensions of the GTM, including an incremental version of the EM algorithm for estimating the model parameters, the use of local subspace models, extensions to mixed discrete and continuous data, semi-linear models which permit the use of high-dimensional manifolds whilst avoiding computational intractability, Bayesian inference applied to hyper-parameters, and an alternative framework for the GTM based on Gaussian processes. All of these developments directly exploit the probabilistic structure of the GTM, thereby allowing the underlying modelling assumptions to be made explicit. They also highlight the advantages of adopting a consistent probabilistic framework for the formulation of pattern recognition algorithms.

Original language	English
Pages (from-to)	203-224
Number of pages	22
Journal	Neurocomputing
Volume	21
Issue number	1-3
DOIs	https://doi.org/10.1016/S0925-2312(98)00043-5
Publication status	Published - 6 Nov 1998

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Bishop, Christopher M.; Svensén, Markus and Williams, Christopher K. I. (1998). Developments of the generative topographic mapping. Neurocomputing, 21 (1-3), pp. 203-224. DOI 10.1016/S0925-2312(98)00043-5

Keywords

Bayesian inference
EM algorithm
generative topographic mapping
local subspace models
semilinear models

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10.1016/S0925-2312(98)00043-5

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title = "Developments of the generative topographic mapping",

abstract = "The generative topographic mapping (GTM) model was introduced by Bishop et al. (1998, Neural Comput. 10(1), 215-234) as a probabilistic re- formulation of the self-organizing map (SOM). It offers a number of advantages compared with the standard SOM, and has already been used in a variety of applications. In this paper we report on several extensions of the GTM, including an incremental version of the EM algorithm for estimating the model parameters, the use of local subspace models, extensions to mixed discrete and continuous data, semi-linear models which permit the use of high-dimensional manifolds whilst avoiding computational intractability, Bayesian inference applied to hyper-parameters, and an alternative framework for the GTM based on Gaussian processes. All of these developments directly exploit the probabilistic structure of the GTM, thereby allowing the underlying modelling assumptions to be made explicit. They also highlight the advantages of adopting a consistent probabilistic framework for the formulation of pattern recognition algorithms.",

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author = "Bishop, {Christopher M.} and Markus Svens{\'e}n and Williams, {Christopher K. I.}",

note = "NOTICE: this is the author{\textquoteright}s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Bishop, Christopher M.; Svens{\'e}n, Markus and Williams, Christopher K. I. (1998). Developments of the generative topographic mapping. Neurocomputing, 21 (1-3), pp. 203-224. DOI 10.1016/S0925-2312(98)00043-5",

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Developments of the generative topographic mapping

Abstract

Bibliographical note

Keywords

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