The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
GTM: The Generative Topographic Mapping
Abstract
Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis, which is based on a linear transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm. GTM provides a principled alternative to the widely used self-organizing map (SOM) of Kohonen (1982) and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multiphase oil pipeline.
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Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
A Stochastic Approximation Method
Robbins, H., & Monro, S. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729586 · Cited by 9,643
Self-organized formation of topologically correct feature maps
Kohonen, T. (1982) · Biological Cybernetics · doi:10.1007/bf00337288 · Cited by 9,529
Nadaraya, E. A. (1964) · Theory of Probability & Its Applications · doi:10.1137/1109020 · Cited by 3,462
Cited by
Nonlinear Dimensionality Reduction by Locally Linear Embedding
Roweis, S. T., & Saul, L. K. (2000) · Science · doi:10.1126/science.290.5500.2323 · Cited by 14,965
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
Gaussian Processes for Machine Learning
Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
Self-citationDeep Unsupervised Learning using Nonequilibrium Thermodynamics
Sohl-Dickstein, J., Weiss, E. A., Maheswaranathan, N., & Ganguli, S. (2015) · arXiv · doi:10.48550/arxiv.1503.03585 · Cited by 2,637
(2002) · Cited by 1,635
Metadata
- Authors
- Bishop, C. M., Svensén, M., & Williams, C. K. I.
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 1998-01-01
- Volume
- 10
- Issue
- 1
- Pages
- 215-234
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2107636931
- Cited by
- 1,388
- References
- 4
- FWCI
- 49.88
- Type
- journal article
- Language
- en
- Open access
- closed
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- Bishop, C. M., Svensén, M., & Williams, C. K. I. (1998). GTM: The Generative Topographic Mapping. Neural Computation. https://doi.org/10.1162/089976698300017953
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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