### Abstract

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

Pages (from-to) | 215-235 |

Number of pages | 21 |

Journal | Neural Computation |

Volume | 10 |

Issue number | 1 |

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

*Neural Computation*,

*10*(1), 215-235.

}

*Neural Computation*, vol. 10, no. 1, pp. 215-235.

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

Research output: Contribution to journal › Article

TY - JOUR

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

UR - http://www.mitpressjournals.org/doi/abs/10.1162/089976698300017953?prevSearch=allfield%3A%28bishop%2C+williams%29&searchHistoryKey=

UR - http://www.scopus.com/inward/record.url?scp=0347963789&partnerID=8YFLogxK

M3 - Article

VL - 10

SP - 215

EP - 235

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 1

ER -