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Investigation of proportional link linkage clustering methods

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Abstract

Proportional link linkage (PLL) clustering methods are a parametric family of monotone invariant agglomerative hierarchical clustering methods. This family includes the single, minimedian, and complete linkage clustering methods as special cases; its members are used in psychological and ecological applications. Since the literature on clustering space distortion is oriented to quantitative input data, we adapt its basic concepts to input data with only ordinal significance and analyze the space distortion properties of PLL methods. To enable PLL methods to be used when the numbern of objects being clustered is large, we describe an efficient PLL algorithm that operates inO(n 2 logn) time andO(n 2) space.

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Authors and Affiliations

  1. Department of Computer Science, Memorial University of Newfoundland, A1C 5S7, St. John's, Newfoundland, Canada

    William H. E. Day

  2. Institute für Informationsverarbeitung, Technische Universität Graz, Schiesstattgasse 4a, A-8010, Graz, Austria

    Herbert Edelsbrunner

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  1. William H. E. Day
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  2. Herbert Edelsbrunner
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Additional information

This work was partially supported by the Natural Sciences and Engineering Research Council of Canada and by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung.

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Day, W.H.E., Edelsbrunner, H. Investigation of proportional link linkage clustering methods. Journal of Classification 2, 239–254 (1985). https://doi.org/10.1007/BF01908077

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