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Prepyramidal clustering and Robinsonian dissimilarities: one-to-one correspondences

Bertrand, Patrice; Diatta, Jean (2013), Prepyramidal clustering and Robinsonian dissimilarities: one-to-one correspondences, Wiley Interdisciplinary Reviews. Data Mining and Knowledge Discovery, 3, 4, p. 290-297. http://dx.doi.org/10.1002/widm.1096

Type
Article accepté pour publication ou publié
Date
2013
Journal name
Wiley Interdisciplinary Reviews. Data Mining and Knowledge Discovery
Volume
3
Number
4
Publisher
Wiley
Pages
290-297
Publication identifier
http://dx.doi.org/10.1002/widm.1096
Metadata
Show full item record
Author(s)
Bertrand, Patrice
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Diatta, Jean
Institut de REcherche en Mathématiques et Informatique Appliquées [IREMIA]
Abstract (EN)
Cluster analysis and seriation are basic data mining techniques. We consider here clustering structures that enable us to achieve both a clustering and a seriation, namely the hierarchical, pyramidal, and prepyramidal clustering structures. Cluster collections of these types determine seriations of any data set by providing compatible orders, i.e., total rankings of the whole data set for which the objects within each cluster are consecutive. Moreover, the dissimilarity measures induced from such cluster collections are Robinsonian; in other words, the more distant the objects in a compatible order, the higher the induced dissimilarity value. It results in a one-to-one correspondence between weakly indexed pyramids and the class of Robinsonian dissimilarities, which holds still in a general setting where undistinguishable objects can be detected, and, as shown in this paper, extends, to prepyramids, which are not required to contain arbitrary intersections of clusters.
Subjects / Keywords
Hierarchical Clustering; Robinsonian dissimilarity; Pyramidal Clustering; Seriation

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