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Mixed integer linear programming formulation for K-means clustering problem

Author

Listed:
  • Kolos Cs. Ágoston

    (Corvinus University of Budapest)

  • Marianna E.-Nagy

    (Corvinus University of Budapest)

Abstract

The minimum sum-of-squares clusering is the most widely used clustering method. The minimum sum-of-squares clustering is usually solved by the heuristic KMEANS algorithm, which converges to a local optimum. A lot of effort has been made to solve such kind of problems, but a mixed integer linear programming formulation (MILP) is still missing. In this paper, we formulate MILP models. The advantage of MILP formulation is that users can extend the original problem with arbitrary linear constraints. We also present numerical results, we solve these models up to sample size of 150.

Suggested Citation

  • Kolos Cs. Ágoston & Marianna E.-Nagy, 2024. "Mixed integer linear programming formulation for K-means clustering problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(1), pages 11-27, March.
    • Handle: RePEc:spr:cejnor:v:32:y:2024:i:1:d:10.1007_s10100-023-00881-1
    DOI: 10.1007/s10100-023-00881-1
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    References listed on IDEAS

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    1. Snježana Majstorović & Kristian Sabo & Johannes Jung & Matija Klarić, 2018. "Spectral methods for growth curve clustering," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 715-737, September.
    2. CORNUEJOLS, Gérard & NEMHAUSER, George L. & WOLSEY, Laurence A., 1980. "A canonical representation of simple plant location problems and its applications," LIDAM Reprints CORE 414, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. J. A. Hartigan & M. A. Wong, 1979. "A K‐Means Clustering Algorithm," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 100-108, March.
    4. Kulkarni, Girish & Fathi, Yahya, 2007. "Integer programming models for the q-mode problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 612-625, October.
    5. Ulrich Dorndorf & Erwin Pesch, 1994. "Fast Clustering Algorithms," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 141-153, May.
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