### Abstract

Original language | English |
---|---|

Place of Publication | Birmingham |

Publisher | Aston University |

Number of pages | 16 |

ISBN (Print) | NCRG/96/015 |

Publication status | Published - 1 Jan 1998 |

### Fingerprint

### Keywords

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

### Cite this

*GTM: the generative topographic mapping*. Birmingham: Aston University.

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**GTM: the generative topographic mapping.** / Bishop, Christopher M.; Svensén, Markus; Williams, Christopher K. I.

Research output: Working paper › Technical report

TY - UNPB

T1 - GTM: the generative topographic mapping

AU - Bishop, Christopher M.

AU - Svensén, Markus

AU - Williams, Christopher K. I.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

KW - Latent variable models

KW - probability density

KW - variables

KW - linear transformations

KW - latent space

KW - data space

KW - non-linear

KW - generative topographic mapping

KW - EM algorithm

KW - elf-Organizing Map

M3 - Technical report

SN - NCRG/96/015

BT - GTM: the generative topographic mapping

PB - Aston University

CY - Birmingham

ER -