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Hierarchies and Weak-hierarchies as Interval Convexities

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBertrand, Patrice
hal.structure.identifierLaboratoire d'Informatique et de Mathématiques [LIM]
dc.contributor.authorDiatta, Jean
dc.date.accessioned2023-01-12T12:33:42Z
dc.date.available2023-01-12T12:33:42Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23685
dc.language.isoenen
dc.subjectWeak hierarchyen
dc.subjectinterval convexityen
dc.subjectSingle Link hierarchyen
dc.subject.ddc515en
dc.titleHierarchies and Weak-hierarchies as Interval Convexitiesen
dc.typeCommunication / Conférence
dc.description.abstractenHierarchies and weak-hierarchies as interval convexities P. Bertrand and J. Diatta There are several ways to characterize a hierarchy, one being a collection of nonempty subsets that are convex according to a type of interval function. This characterization in terms of interval convexity, extends to general classes of multilevel clusterings, thus providing a unifying heoretical framework [1, 2]. We expand this line of research, with a special attention to specifications allowing the capture of clusterings usually constructed in data mining practice, such as the Apresjan and the single-link hierarchies. We propose: (a) New characterizations of hierarchies and weak hierarchies as interval convexities, (b) Interval functions which induce known clustering schemes such as the Single Link hierarchy or the Apresjan hierarchy, (c) A sequence of nested families of interval convexities that is gradually increasing from the Apresjan hierarchy to the Single-Link hierarchy, which enables the detection of redundant clusters.en
dc.subject.ddclabelAnalyseen
dc.relation.conftitle17th Conference of the International Federation of Classification Societiesen
dc.relation.confdate2022-07
dc.relation.confcityPortoen
dc.relation.confcountryPortugalen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidateouien
dc.description.readershipnon-rechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2023-01-12T12:30:46Z
hal.identifierhal-03935954
hal.version1
hal.date.transferred2023-01-12T12:33:44Z
hal.author.functionaut
hal.author.functionaut


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