Show simple item record

dc.contributor.authorBertrand, Patrice
dc.contributor.authorDiatta, Jean
dc.date.accessioned2017-11-30T11:16:23Z
dc.date.available2017-11-30T11:16:23Z
dc.date.issued2017
dc.identifier.issn0166-218X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17117
dc.language.isoenen
dc.subjectAbstract convexity
dc.subjectInterval operator
dc.subjectPyramidal clustering model
dc.subjectweak hierarchy
dc.subjectPaired hierarchy
dc.subject.ddc519en
dc.titleMultilevel clustering models and interval convexities
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe -weakly hierarchical, pyramidal and paired hierarchical models are alternative multilevel clustering models that extend hierarchical clustering. In this paper, we study these various multilevel clustering models in the framework of general convexity. We prove a characterization of the paired hierarchical model via a four-point condition on the segment operator, and examine the case of -weakly hierarchical models for . We also prove sufficient conditions for an interval convexity to be either hierarchical, paired hierarchical, pyramidal, weakly hierarchical or -weakly hierarchical. Moreover, we propose a general algorithm for computing the interval convexity induced by any given interval operator, and deduce a unified clustering scheme for capturing either of the considered multilevel clustering models. We illustrate our results with two interval operators that can be defined from any dissimilarity index and propose a parameterized definition of an adaptive interval operator for cluster analysis.
dc.relation.isversionofjnlnameDiscrete Applied Mathematics
dc.relation.isversionofjnlvol222
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages54-66
dc.relation.isversionofdoi10.1016/j.dam.2016.12.019
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T17:55:04Z


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record