### Abstract

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.

Original language | English |
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Place of Publication | Birmingham |

Publisher | Aston University |

Number of pages | 6 |

ISBN (Print) | NCRG/96/031 |

Publication status | Published - 15 Apr 1997 |

### 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

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## Cite this

Bishop, C. M., Svens'en, M., Williams, C. K. I., von der Malsburg, C., von Selen, W., Vorbruggen, J. C., & Sendhoff, B. (1997).

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