An Order Theoretic Model for Cluster Analysis

To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model due to N. Jardine and R. Sibson. Some of its salient properties are established, with special attention paid to the incorporation of Jardine...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 34; no. 1; pp. 55 - 72
Main Author Janowitz, M. F.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.1978
Subjects
Axioms
Classification
Cluster analysis
Equivalence relation
Geology
Homomorphisms
Mathematical models
Modeling
Partially ordered sets
Real numbers
Topology
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ISSN0036-1399
1095-712X
DOI10.1137/0134005

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Summary:To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model due to N. Jardine and R. Sibson. Some of its salient properties are established, with special attention paid to the incorporation of Jardine and Sibson's "flat" cluster methods into the model. It is shown how the characterization of flat cluster methods leads to a universal mapping problem in the theory of partially ordered sets. This problem is solved, and its solution applied both to the present model and to the Jardine-Sibson model.
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ISSN:0036-1399
1095-712X
DOI:10.1137/0134005