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The k-weak hierarchical representations: an extension of the indexed closed weak hierarchies

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBertrand, Patrice*
hal.structure.identifierCenter for Discrete Mathematics and Theoretical Computer Science [Rutgers] [DIMACS]
dc.contributor.authorJanowitz, Melvin F.*
dc.date.accessioned2009-10-01T11:45:04Z
dc.date.available2009-10-01T11:45:04Z
dc.date.issued2003
dc.identifier.issn0166-218X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/2051
dc.language.isoenen
dc.subjectDiscrete Mathematics
dc.subjectCluster Analysis
dc.subject.ddc519en
dc.titleThe k-weak hierarchical representations: an extension of the indexed closed weak hierarchies
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDIMACS, Rutgers The State University;États-Unis
dc.description.abstractenSeveral approaches have been proposed for the purpose of proving that different classes of dissimilarities (e.g. ultrametrics) can be represented by certain types of stratified clusterings which are easily visualized (e.g. indexed hierarchies). These approaches differ in the choice of the clusters that are used to represent a dissimilarity coefficient. More precisely, the clusters may be defined as the maximal linked subsets, also called ML-sets; equally they may be defined as a particular type of 2-ball. In this paper, we first introduce the notion of a k-ball, thereby extending the notion of a 2-ball. For an arbitrary dissimilarity coefficient, we establish some properties of the k-balls that pinpoint the connection between them and the ML-sets. We also introduce the (2,k)-point condition (kgreater-or-equal, slanted1) which is an extension of the Bandelt four-point condition.For kgreater-or-equal, slanted2, we prove that the dissimilarities satisfying the (2,k)-point condition are in one–one correspondence with a class of stratified clusterings, called k-weak hierarchical representations, whose main characteristic is that the intersection of (k+1) arbitrary clusters may be reduced to the intersection of some k of these clusters.
dc.relation.isversionofjnlnameDiscrete Applied Mathematics
dc.relation.isversionofjnlvol127
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2003
dc.relation.isversionofjnlpages199-220
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/S0166-218X(02)00206-8
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2019-09-16T12:53:11Z
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