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Reports (Research Report) Year : 2009

Directed binary hierarchies and directed ultrametrics

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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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Dates and versions

inria-00361727 , version 1 (16-02-2009)
inria-00361727 , version 2 (26-02-2009)

Identifiers

  • HAL Id : inria-00361727 , version 2

Cite

Israël-César Lerman, Pascale Kuntz. Directed binary hierarchies and directed ultrametrics. [Research Report] RR-6815, INRIA. 2009, pp.27. ⟨inria-00361727v2⟩
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