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### 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 transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM 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 multi-phase oil pipeline.

Original language | English |
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Pages (from-to) | 215-235 |

Number of pages | 21 |

Journal | Neural Computation |

Volume | 10 |

Issue number | 1 |

Publication status | Published - 1 Jan 1998 |

### Keywords

- Latent variable models
- probability density
- variables
- linear transformations
- latent space
- data space
- non-linear
- generative topographic mapping
- EM algorithm
- elf-Organizing Map

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## Research Output

- 1 Technical report

## GTM: the generative topographic mapping

Bishop, C. M., Svensén, M. & Williams, C. K. I., 1 Jan 1998, Birmingham: Aston University, 16 p.Research output: Working paper › Technical report

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## Cite this

Bishop, C. M., Svensén, M., & Williams, C. K. I. (1998). GTM: the generative topographic mapping.

*Neural Computation*,*10*(1), 215-235.