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The seeding algorithm for k-means problem with penalties

Author

Listed:
  • Min Li

    (Shandong Normal University)

  • Dachuan Xu

    (Beijing University of Technology)

  • Jun Yue

    (Shandong Normal University)

  • Dongmei Zhang

    (Shandong Jianzhu University)

  • Peng Zhang

    (Shandong University)

Abstract

The k-means problem is a classic NP-hard problem in machine learning and computational geometry. And its goal is to separate the given set into k clusters according to the minimal squared distance. The k-means problem with penalties, as one generalization of k-means problem, allows that some point need not be clustered instead of being paid some penalty. In this paper, we study the k-means problem with penalties by using the seeding algorithm. We propose that the accuracy only involves the ratio of the maximal penalty value to the minimal one. When the penalty is uniform, the approximation factor reduces to the same one for the k-means problem. Moreover, our result generalizes the k-means++ for k-means problem to the penalty version. Numerical experiments show that our seeding algorithm is more effective than the one without using seeding.

Suggested Citation

  • Min Li & Dachuan Xu & Jun Yue & Dongmei Zhang & Peng Zhang, 2020. "The seeding algorithm for k-means problem with penalties," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 15-32, January.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:1:d:10.1007_s10878-019-00450-w
    DOI: 10.1007/s10878-019-00450-w
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    Citations

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    Cited by:

    1. Sai Ji & Dachuan Xu & Longkun Guo & Min Li & Dongmei Zhang, 0. "The seeding algorithm for spherical k-means clustering with penalties," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-18.
    2. Min Li, 2022. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1693-1704, October.
    3. Peihuang Huang & Pei Yao & Zhendong Hao & Huihong Peng & Longkun Guo, 2021. "Improved Constrained k -Means Algorithm for Clustering with Domain Knowledge," Mathematics, MDPI, vol. 9(19), pages 1-14, September.
    4. Sai Ji & Dachuan Xu & Longkun Guo & Min Li & Dongmei Zhang, 2022. "The seeding algorithm for spherical k-means clustering with penalties," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1977-1994, October.
    5. Min Li, 0. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.
    6. Xiaoyun Tian & Dachuan Xu & Donglei Du & Ling Gai, 2022. "The spherical k-means++ algorithm via local search scheme," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2375-2394, November.

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