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Directed binary hierarchies and directed ultrametrics

Israël-César Lerman 1 Pascale Kuntz 2
1 SYMBIOSE - Biological systems and models, bioinformatics and sequences
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : 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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Submitted on : Monday, February 16, 2009 - 3:00:40 PM
Last modification on : Thursday, November 15, 2018 - 11:57:19 AM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 10:32:53 PM


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  • HAL Id : inria-00361727, version 1


Israël-César Lerman, Pascale Kuntz. Directed binary hierarchies and directed ultrametrics. [Research Report] RR-6815, 2009, pp.27. ⟨inria-00361727v1⟩



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