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Article Dans Une Revue Journal of Classification Année : 2011

Directed Binary Hierarchies and Directed Ultrametrics

Résumé

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 the classical binary hierarchical classification in a very specific way. In this paper an accurate formalization of this new structure is studied. A directed hierarchy is defined as a set of ordered pairs of subsets of the initial individual set satisfying specific conditions. A new notion of directed ultrametricity is studied. The main result consists in establishing a bijective correspondence between a directed ultrametric space and a directed binary hierarchy. Finally, an algorithm is proposed in order to transform a directed ultrametric structure into a graphical representation associated with a directed binary hierarchy.

Dates et versions

hal-00643982 , version 1 (23-11-2011)

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Israël-César C. Lerman, Pascale Kuntz. Directed Binary Hierarchies and Directed Ultrametrics. Journal of Classification, 2011, 28 (3), pp.272-296. ⟨10.1007/s00357-011-9091-y⟩. ⟨hal-00643982⟩
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