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Weak Hierarchies: A Central Clustering Structure

dc.contributor.authorBertrand, Patrice
dc.contributor.authorDiatta, Jean
dc.date.accessioned2014-06-16T12:24:10Z
dc.date.available2014-06-16T12:24:10Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13462
dc.language.isoenen
dc.subjectWeak hierarchyen
dc.subjectQuasi-ultrametricen
dc.subject2-Ballen
dc.subjectWeak clusteren
dc.subjectFormal concepten
dc.subject.ddc518en
dc.titleWeak Hierarchies: A Central Clustering Structureen
dc.typeChapitre d'ouvrage
dc.description.abstractenThe k-weak hierarchies, for k ≥ 2, are the cluster collections such that the intersection of any (k + 1) members equals the intersection of some k of them. Any cluster collection turns out to be a k-weak hierarchy for some integer k. Weak hierarchies play a central role in cluster analysis in several aspects: they are defined as the 2-weak hierarchies, so that they not only extend directly the well-known hierarchical structure, but they are also characterized by the rank of their closure operator which is at most 2. The main aim of this chapter is to present, in a unique framework, two distinct weak hierarchical clustering approaches. The first one is based on the idea that, since clusters must be isolated, it is natural to determine them as weak clusters defined by a positive weak isolation index. The second one determines the weak subdominant quasi-ultrametric of a given dissimilarity, and thus an optimal closed weak hierarchy by means of the bijection between quasi-ultrametrics and (indexed) closed weak hierarchies. Furthermore, we highlight the relationship between weak hierarchical clustering and formal concepts analysis, through which concept extents appear to be weak clusters of some multiway dissimilarity functions.en
dc.identifier.citationpages211-230en
dc.relation.ispartoftitleClusters, Orders, and Trees: Methods and Applicationsen
dc.relation.ispartofeditorAleskerov, Fuad
dc.relation.ispartofeditorGoldengorin, Boris
dc.relation.ispartofeditorPardalos, Panos M.
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlinen
dc.relation.ispartofdate2014
dc.relation.ispartofpages404en
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-1-4939-0742-7en
dc.subject.ddclabelModèles mathématiques. Algorithmesen
dc.relation.ispartofisbn978-1-4939-0741-0en
dc.relation.forthcomingnonen
dc.identifier.doihttp://dx.doi.org/10.1007/978-1-4939-0742-7_14en


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