### Abstract

Compact graph based representation of complex data can be used for clustering and visualisation. In this chapter we introduce basic concepts of graph theory and present approaches which may generate graphs from data. Computational complexity of clustering and visualisation algorithms can be reduced replacing original objects with their representative elements (code vectors or fingerprints) by vector quantisation. We introduce widespread vector quantisation methods, the k -means and the neural gas algorithms. Topology representing networks obtained by the modification of neural gas algorithm create graphs useful for the low-dimensional visualisation of data set. In this chapter the basic algorithm of the topology representing networks and its variants (Dynamic Topology Representing Network and Weighted Incremental Neural Network) are presented in details.

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

Title of host publication | SpringerBriefs in Computer Science |

Publisher | Springer |

Pages | 1-16 |

Number of pages | 16 |

Edition | 9781447151579 |

DOIs | |

Publication status | Published - Jan 1 2013 |

### Publication series

Name | SpringerBriefs in Computer Science |
---|---|

Number | 9781447151579 |

ISSN (Print) | 2191-5768 |

ISSN (Electronic) | 2191-5776 |

### Fingerprint

### Keywords

- Cluster centre
- Delaunay triangulation
- Minimal span tree
- Vector quantisation
- Voronoi diagram

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*SpringerBriefs in Computer Science*(9781447151579 ed., pp. 1-16). (SpringerBriefs in Computer Science; No. 9781447151579). Springer. https://doi.org/10.1007/978-1-4471-5158-6_1

**Vector quantisation and topology based graph representation.** / Vathy-Fogarassy, Ágnes; Abonyi, J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*SpringerBriefs in Computer Science.*9781447151579 edn, SpringerBriefs in Computer Science, no. 9781447151579, Springer, pp. 1-16. https://doi.org/10.1007/978-1-4471-5158-6_1

}

TY - CHAP

T1 - Vector quantisation and topology based graph representation

AU - Vathy-Fogarassy, Ágnes

AU - Abonyi, J.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Compact graph based representation of complex data can be used for clustering and visualisation. In this chapter we introduce basic concepts of graph theory and present approaches which may generate graphs from data. Computational complexity of clustering and visualisation algorithms can be reduced replacing original objects with their representative elements (code vectors or fingerprints) by vector quantisation. We introduce widespread vector quantisation methods, the k -means and the neural gas algorithms. Topology representing networks obtained by the modification of neural gas algorithm create graphs useful for the low-dimensional visualisation of data set. In this chapter the basic algorithm of the topology representing networks and its variants (Dynamic Topology Representing Network and Weighted Incremental Neural Network) are presented in details.

AB - Compact graph based representation of complex data can be used for clustering and visualisation. In this chapter we introduce basic concepts of graph theory and present approaches which may generate graphs from data. Computational complexity of clustering and visualisation algorithms can be reduced replacing original objects with their representative elements (code vectors or fingerprints) by vector quantisation. We introduce widespread vector quantisation methods, the k -means and the neural gas algorithms. Topology representing networks obtained by the modification of neural gas algorithm create graphs useful for the low-dimensional visualisation of data set. In this chapter the basic algorithm of the topology representing networks and its variants (Dynamic Topology Representing Network and Weighted Incremental Neural Network) are presented in details.

KW - Cluster centre

KW - Delaunay triangulation

KW - Minimal span tree

KW - Vector quantisation

KW - Voronoi diagram

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U2 - 10.1007/978-1-4471-5158-6_1

DO - 10.1007/978-1-4471-5158-6_1

M3 - Chapter

T3 - SpringerBriefs in Computer Science

SP - 1

EP - 16

BT - SpringerBriefs in Computer Science

PB - Springer

ER -