### Abstract

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

Place of Publication | Birmingham |

Publisher | Aston University |

Number of pages | 6 |

ISBN (Print) | NCRG/96/031 |

Publication status | Published - 15 Apr 1997 |

### Fingerprint

### Keywords

- self-organizing map
- algorithm
- heuristic ideas
- density of data
- latent variable model
- Generative Topographic Mapping
- non-linear transformations
- latent space
- data space
- expectation-maximization

### Cite this

*GTM: A principled alternative to the self-organizing map*. Birmingham: Aston University.

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**GTM: A principled alternative to the self-organizing map.** / Bishop, Christopher M.; Svens'en, M.; Williams, Christopher K. I.; von der Malsburg, C.; von Selen, W.; Vorbruggen, J. C.; Sendhoff, B.

Research output: Working paper › Technical report

TY - UNPB

T1 - GTM: A principled alternative to the self-organizing map

AU - Bishop, Christopher M.

AU - Svens'en, M.

AU - Williams, Christopher K. I.

AU - von der Malsburg, C.

AU - von Selen, W.

AU - Vorbruggen, J. C.

AU - Sendhoff, B.

PY - 1997/4/15

Y1 - 1997/4/15

N2 - The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general non-linear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multi-phase oil pipeline.

AB - The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general non-linear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multi-phase oil pipeline.

KW - self-organizing map

KW - algorithm

KW - heuristic ideas

KW - density of data

KW - latent variable model

KW - Generative Topographic Mapping

KW - non-linear transformations

KW - latent space

KW - data space

KW - expectation-maximization

M3 - Technical report

SN - NCRG/96/031

BT - GTM: A principled alternative to the self-organizing map

PB - Aston University

CY - Birmingham

ER -