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| HAL : inria-00361727, version 2 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Versions disponibles | v1 (16-02-2009) | v2 (27-02-2009) |
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| Directed binary hierarchies and directed ultrametrics |
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| Israël-César Lerman 1Pascale Kuntz 2 |
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| (2009) |
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| Directed binary hierarchies have been introduced in order to give a graphical reduced representation of a family of association rules. This type of structure extends in a very specific way that underlying binary hierarchical classification. In this paper an accurate formalization of this new structure is studied. A binary directed hierarchy is defined as a set of ordered pairs of subsets of the initial individual set satisfying specific conditions. New notion of directed ultrametricity is studied. The main result consists of establishing a bijective correspondence between a directed ultrametric space and a directed binary hierarchy. Moreover, an algorithm is proposed in order to transform a directed ultrametric structure into a graphical representation associated with a directed binary hierarchy. |
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| 1 : | SYMBIOSE (INRIA - IRISA) |
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CNRS : UMR6074 – INRIA – Institut National des Sciences Appliquées (INSA) - Rennes – Université de Rennes 1 |
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| 2 : | Laboratoire d'Informatique de Nantes Atlantique (LINA) |
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CNRS : UMR6241 – Université de Nantes – École Nationale Supérieure des Mines - Nantes |
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| Domaine | : | Mathématiques/Combinatoire Informatique/Apprentissage |
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| Oriented ascendant hierarchical classification – Ultrametric spaces – Association rules – Graphical representation |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00361727, version 2 | |
| http://hal.inria.fr/inria-00361727 | |
| oai:hal.inria.fr:inria-00361727 | |
| Contributeur : Anne Jaigu | |
| Soumis le : Jeudi 26 Février 2009, 15:51:43 | |
| Dernière modification le : Vendredi 27 Février 2009, 15:30:06 | |
