Ordinal and percentile clustering
type: Item
instance of: scholarly article
title: Ordinal and percentile clustering
zbMATH Open document ID: 0695.62144
DOI: 10.1016/0165-4896(89)90043-7
published in: Mathematical Social Sciences
publication date: 1989-01-01T00:00:00Z
review text: The purpose of the paper is to put together the basic ideas of the theory of ordinal clustering, as developed by the first author et al. (1978), and the theory of probabilistic metric spaces, as developed by the second author et al. (1983). The principal result is a new theory of clustering, called percentile clustering, in which clustering is based, not on some average or other typical value of the data, but directly on the distributed data itself. In the case of the Jardine-Sibson model [\textit{N. Jardine} and \textit{R. Sibson}, Mathematical Taxonomy, Wiley, N.Y. (1971)] this leads from dissimilarity coefficients (DC) to percentile dissimilarity coefficients (PDC) - and from a totally ordered set to a lattice. Each PDC determines a family of ordinary DC's - one for each percentile c in [0,1]. A secondary outgrowth is a generalized theory of ordinal clustering. A number of algorithms that implement percentile clustering is presented. The paper concludes by applying the new cluster methods to two concrete examples. The first of these is a data set concerning combat death in the Vietnam War; the second is a data set dealing with the classification of species of gibbons. In both instances results obtained with various standard clustering techniques are also presented.
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 4139064
zbMATH Keywords: fuzzy clustering
zbMATH Keywords: distribution functions
zbMATH Keywords: residuated maps
zbMATH Keywords: probabilistic metric spaces
zbMATH Keywords: percentile clustering
zbMATH Keywords: Jardine-Sibson model
zbMATH Keywords: percentile dissimilarity coefficients
zbMATH Keywords: lattice
zbMATH Keywords: generalized theory of ordinal clustering
zbMATH Keywords: algorithms
zbMATH Keywords: classification
author: Melvin F. Janowitz
author: Berthold Schweizer
MaRDI profile type: Publication
full work available at URL: 0165-4896(89)90043-7
OpenAlex ID: W1979671533
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description: scientific article; zbMATH DE number 4139064