### Abstract

We define the γ-observable neighbourhood and use it in soft-competitive learning for vector quantization. Considering a datum v and a set of n units w_{i} in a Euclidean space, let v_{i} be a point of the segment [vw_{i}] whose position depends on γ a real number between 0 and 1, the γ-observable neighbours (γ-ON) of v are the units w_{i} for which v_{i} is in the Voronoï of w_{i}, i.e. w_{i} is the closest unit to v_{i}. For γ=1, v_{i} merges with w_{i}, all the units are γ-ON of v, while for γ=0, v_{i} merges with v, only the closest unit to v is its γ-ON. The size of the neighbourhood decreases from n to 1 while γ goes from 1 to 0. For γ lower or equal to 0.5, the γ-ON of v are also its natural neighbours, i.e. their Voronoï regions share a common boundary with that of v. We show that this neighbourhood used in Vector Quantization gives faster convergence in terms of number of epochs and similar distortion than the Neural-Gas on several benchmark databases, and we propose the fact that it does not have the dimension selection property could explain these results. We show it also presents a new self-organization property we call 'self-distribution'.

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

Pages (from-to) | 1017-1027 |

Number of pages | 11 |

Journal | Neural Networks |

Volume | 15 |

Issue number | 8-9 |

DOIs | |

Publication status | Published - Oct 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- γ-Observable neighbours
- Dimension selection
- Natural neighbours
- Neural-gas
- Self-distribution
- Self-organizing maps
- Vector quantization

### ASJC Scopus subject areas

- Artificial Intelligence
- Neuroscience(all)

### Cite this

*Neural Networks*,

*15*(8-9), 1017-1027. https://doi.org/10.1016/S0893-6080(02)00076-X

**γ-Observable neighbours for vector quantization.** / Aupetit, Michael; Couturier, Pierre; Massotte, Pierre.

Research output: Contribution to journal › Article

*Neural Networks*, vol. 15, no. 8-9, pp. 1017-1027. https://doi.org/10.1016/S0893-6080(02)00076-X

}

TY - JOUR

T1 - γ-Observable neighbours for vector quantization

AU - Aupetit, Michael

AU - Couturier, Pierre

AU - Massotte, Pierre

PY - 2002/10

Y1 - 2002/10

N2 - We define the γ-observable neighbourhood and use it in soft-competitive learning for vector quantization. Considering a datum v and a set of n units wi in a Euclidean space, let vi be a point of the segment [vwi] whose position depends on γ a real number between 0 and 1, the γ-observable neighbours (γ-ON) of v are the units wi for which vi is in the Voronoï of wi, i.e. wi is the closest unit to vi. For γ=1, vi merges with wi, all the units are γ-ON of v, while for γ=0, vi merges with v, only the closest unit to v is its γ-ON. The size of the neighbourhood decreases from n to 1 while γ goes from 1 to 0. For γ lower or equal to 0.5, the γ-ON of v are also its natural neighbours, i.e. their Voronoï regions share a common boundary with that of v. We show that this neighbourhood used in Vector Quantization gives faster convergence in terms of number of epochs and similar distortion than the Neural-Gas on several benchmark databases, and we propose the fact that it does not have the dimension selection property could explain these results. We show it also presents a new self-organization property we call 'self-distribution'.

AB - We define the γ-observable neighbourhood and use it in soft-competitive learning for vector quantization. Considering a datum v and a set of n units wi in a Euclidean space, let vi be a point of the segment [vwi] whose position depends on γ a real number between 0 and 1, the γ-observable neighbours (γ-ON) of v are the units wi for which vi is in the Voronoï of wi, i.e. wi is the closest unit to vi. For γ=1, vi merges with wi, all the units are γ-ON of v, while for γ=0, vi merges with v, only the closest unit to v is its γ-ON. The size of the neighbourhood decreases from n to 1 while γ goes from 1 to 0. For γ lower or equal to 0.5, the γ-ON of v are also its natural neighbours, i.e. their Voronoï regions share a common boundary with that of v. We show that this neighbourhood used in Vector Quantization gives faster convergence in terms of number of epochs and similar distortion than the Neural-Gas on several benchmark databases, and we propose the fact that it does not have the dimension selection property could explain these results. We show it also presents a new self-organization property we call 'self-distribution'.

KW - γ-Observable neighbours

KW - Dimension selection

KW - Natural neighbours

KW - Neural-gas

KW - Self-distribution

KW - Self-organizing maps

KW - Vector quantization

UR - http://www.scopus.com/inward/record.url?scp=0036789801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036789801&partnerID=8YFLogxK

U2 - 10.1016/S0893-6080(02)00076-X

DO - 10.1016/S0893-6080(02)00076-X

M3 - Article

VL - 15

SP - 1017

EP - 1027

JO - Neural Networks

JF - Neural Networks

SN - 0893-6080

IS - 8-9

ER -