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A sampling-based exact algorithm for the solution of the minimax diameter clustering problem

Author

Listed:
  • Daniel Aloise

    (École Polytechnique de Montréal)

  • Claudio Contardo

    (ESG UQÀM)

Abstract

We consider the problem of clustering a set of points so as to minimize the maximum intra-cluster dissimilarity, which is strongly NP-hard. Exact algorithms for this problem can handle datasets containing up to a few thousand observations, largely insufficient for the nowadays needs. The most popular heuristic for this problem, the complete-linkage hierarchical algorithm, provides feasible solutions that are usually far from optimal. We introduce a sampling-based exact algorithm aimed at solving large-sized datasets. The algorithm alternates between the solution of an exact procedure on a small sample of points, and a heuristic procedure to prove the optimality of the current solution. Our computational experience shows that our algorithm is capable of solving to optimality problems containing more than 500,000 observations within moderate time limits, this is two orders of magnitude larger than the limits of previous exact methods.

Suggested Citation

  • Daniel Aloise & Claudio Contardo, 2018. "A sampling-based exact algorithm for the solution of the minimax diameter clustering problem," Journal of Global Optimization, Springer, vol. 71(3), pages 613-630, July.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:3:d:10.1007_s10898-018-0634-1
    DOI: 10.1007/s10898-018-0634-1
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    References listed on IDEAS

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    1. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.
    2. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
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    Cited by:

    1. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.
    2. Ana Maria A. C. Rocha & M. Fernanda P. Costa & Edite M. G. P. Fernandes, 2018. "Preface to the Special Issue “GOW’16”," Journal of Global Optimization, Springer, vol. 71(3), pages 441-442, July.
    3. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
    4. Kamlesh Kumar Pandey & Diwakar Shukla, 2022. "Stratified linear systematic sampling based clustering approach for detection of financial risk group by mining of big data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(3), pages 1239-1253, June.

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