# A higher order Hopfield network for vector quantisation

Soper, Alan (1998) *A higher order Hopfield network for vector quantisation.* Neural Computing & Applications, 7 (2). pp. 99-106. ISSN 0941-0643 electronic 1433-3058

## Abstract

A higher order version of the Hopfield neural network is presented which will perform a simple vector quantisation or clustering function. This model requires no penalty terms to impose constraints in the Hopfield energy, in contrast to the usual one where the energy involves only terms quadratic in the state vector. The energy function is shown to have no local minima within the unit hypercube of the state vector so the network only converges to valid final states. Optimisation trials show that the network can consistently find optimal clusterings for small, trial problems and

near optimal ones for a large data set consisting of the intensity values from the digitised, grey-level image.

Item Type: | Article |
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Uncontrolled Keywords: | Clustering; Combinatorial optimisation; Higher Order Neural Networks; Hopfield neural networks, non-linear representation, vector Quantisation, |

Subjects: | Q Science > QA Mathematics |

School / Department / Research Groups: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Computer & Computational Science Research Group School of Computing & Mathematical Sciences > Department of Computer Science School of Computing & Mathematical Sciences > Department of Mathematical Sciences |

Related URLs: | |

Last Modified: | 12 Apr 2011 17:11 |

URI: | http://gala.gre.ac.uk/id/eprint/118 |

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