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Piecewise hierarchical clustering

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Abstract

We consider two or more ultrametric distance matrices defined over different, possibly overlapping, subsets. These matrices are merged into one ultrametric matrix defined over the whole set. Necessary and sufficient conditions for uniqueness of the merging are established. when these conditions are not satisfied, consistent algorithms are given.

Resume

Etant données au moins deux matrices de distances ultramétriques définies sur des sous-ensembles disjoints ou non, on les fusionne pour obtenir une ultramétrique définie sur l'ensemble tout entier. On donne des conditions nécessaires et suffisantes pour que l'extension soit unique. Quand ces conditions ne sont pas satisfaites on donne des algorithmes dont on montre qu'ils sont consistants.

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Authors and Affiliations

  1. Université de Haute-Bretagne Rennes 2, 35043, Rennes cedex, France

    Gildas Brossier

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  1. Gildas Brossier
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The author thanks B. Monjardet and two anonymous referees for their helpful comments.

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Brossier, G. Piecewise hierarchical clustering. Journal of Classification 7, 197–216 (1990). https://doi.org/10.1007/BF01908716

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  • DOI: https://doi.org/10.1007/BF01908716

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