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The Parallel Seeding Algorithm for k-Means Problem with Penalties

Author

Listed:
  • Min Li

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China)

  • Dachuan Xu

    (Department of Operations Research and Scientific Computing, Beijing University of Technology, Beijing 100124, P. R. China)

  • Jun Yue

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China)

  • Dongmei Zhang

    (School of Computer Science and Technology, Shandong Jianzhu University, Jinan 250101, P. R. China)

Abstract

As a classic NP-hard problem in machine learning and computational geometry, the k-means problem aims to partition a data point set into k clusters such that the sum of the squared distance from each point to its nearest center is minimized. The k-means problem with penalties, denoted by k-MPWP, generalizing the k-means problem, allows that some points can be paid some penalties instead of being clustered. In this paper, we study the seeding algorithm of k-MPWP and propose a parallel seeding algorithm for k-MPWP along with the corresponding theoretical analysis.

Suggested Citation

  • Min Li & Dachuan Xu & Jun Yue & Dongmei Zhang, 2020. "The Parallel Seeding Algorithm for k-Means Problem with Penalties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-18, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400059
    DOI: 10.1142/S0217595920400059
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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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