### Abstract

Original language | English |
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Publication status | Published - 1997 |

Event | Proceedings 1997 Workshop on Self-Organizing Maps - Helsinki University of Technology, Finland Duration: 4 Jun 1997 → 6 Jun 1997 |

### Workshop

Workshop | Proceedings 1997 Workshop on Self-Organizing Maps |
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Country | Finland |

City | Helsinki University of Technology |

Period | 4/06/97 → 6/06/97 |

### Fingerprint

### Keywords

- Magnification factors
- topographic mapping
- discrete
- neuro-biological
- Generative Topographic Mapping
- differential geometry
- morphological

### Cite this

*Magnification factors for the SOM and GTM algorithms*. Paper presented at Proceedings 1997 Workshop on Self-Organizing Maps, Helsinki University of Technology, Finland.

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**Magnification factors for the SOM and GTM algorithms.** / Bishop, Christopher M.; Svens'en, Markus; Williams, Christopher K. I.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Magnification factors for the SOM and GTM algorithms

AU - Bishop, Christopher M.

AU - Svens'en, Markus

AU - Williams, Christopher K. I.

PY - 1997

Y1 - 1997

N2 - Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

AB - Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

KW - Magnification factors

KW - topographic mapping

KW - discrete

KW - neuro-biological

KW - Generative Topographic Mapping

KW - differential geometry

KW - morphological

UR - http://www.cis.hut.fi/wsom97/progabstracts/19.html

M3 - Paper

ER -