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An Exact Algorithm for the Two-Mode KL-Means Partitioning Problem

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Abstract

Two-mode partitioning applications are increasingly common in the physical and social sciences with a variety of models and methods spanning these applications. Two-mode KL-means partitioning (TMKLMP) is one type of two-mode partitioning model with a conceptual appeal that stems largely from the fact that it is a generalization of the ubiquitous (one-mode) K-means clustering problem. A number of heuristic methods have been proposed for TMKLMP, ranging from a two-mode version of the K-means heuristic to metaheuristic approaches based on simulated annealing, genetic algorithms, variable neighborhood search, fuzzy steps, and tabu search. We present an exact algorithm for TMKLMP based on branch-and-bound programming and demonstrate its utility for the clustering of brand switching, manufacturing cell formation, and journal citation data. Although the proposed branchand-bound algorithm does not obviate the need for approximation methods for large two-mode data sets, it does provide a first step in the development of methods that afford a guarantee of globally-optimal solutions for TMKLMP.

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Authors and Affiliations

  1. College of Business, Florida State University, Tallahassee, Florida, USA

    Michael J. Brusco

  2. Faculty of Social Sciences, University of Ljubljana, Ljubljana, Slovenia

    Patrick Doreian

  3. Department of Sociology, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

    Patrick Doreian

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  1. Michael J. Brusco
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  2. Patrick Doreian
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Correspondence to Michael J. Brusco or Patrick Doreian.

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Brusco, M.J., Doreian, P. An Exact Algorithm for the Two-Mode KL-Means Partitioning Problem. J Classif 32, 481–515 (2015). https://doi.org/10.1007/s00357-015-9185-z

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  • DOI: https://doi.org/10.1007/s00357-015-9185-z

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