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Clustering and Prediction of Rankings Within a Kemeny Distance Framework

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Algorithms from and for Nature and Life

Abstract

Rankings and partial rankings are ubiquitous in data analysis, yet there is relatively little work in the classification community that uses the typical properties of rankings. We review the broader literature that we are aware of, and identify a common building block for both prediction of rankings and clustering of rankings, which is also valid for partial rankings. This building block is the Kemeny distance, defined as the minimum number of interchanges of two adjacent elements required to transform one (partial) ranking into another. The Kemeny distance is equivalent to Kendall’s τ for complete rankings, but for partial rankings it is equivalent to Emond and Mason’s extension of τ. For clustering, we use the flexible class of methods proposed by Ben-Israel and Iyigun (Journal of Classification 25: 5–26, 2008), and define the disparity between a ranking and the center of cluster as the Kemeny distance. For prediction, we build a prediction tree by recursive partitioning, and define the impurity measure of the subgroups formed as the sum of all within-node Kemeny distances. The median ranking characterizes subgroups in both cases.

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Notes

  1. 1.

    During the Frankfurt DAGM-GfKl-2011-conference, Eyke Hüllermeier kindly pointed out that there is related work in the computer science community under the name “preference learning” (in particular, Cheng et al. (2009), and more generally, Fürnkranz and Hüllermeier 2010).

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Authors and Affiliations

  1. Institute of Psychology, Leiden University, 2300 RB, Leiden, The Netherlands

    Willem J. Heiser

  2. Department of Industrial Engineering, University of Naples Federico II, Piazzale Tecchio, 80125, Naples, Italy

    Antonio D’Ambrosio

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  1. Willem J. Heiser
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  2. Antonio D’Ambrosio
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Correspondence to Willem J. Heiser .

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Editors and Affiliations

  1. University of Essex Department of Mathematical Sciences, Colchester, United Kingdom

    Berthold Lausen

  2. Ghent University Department of Marketing, Ghent, Belgium

    Dirk Van den Poel

  3. University of Marburg Databionics, FB 12, Marburg, Germany

    Alfred Ultsch

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Heiser, W.J., D’Ambrosio, A. (2013). Clustering and Prediction of Rankings Within a Kemeny Distance Framework. In: Lausen, B., Van den Poel, D., Ultsch, A. (eds) Algorithms from and for Nature and Life. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-00035-0_2

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