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Approximation Algorithms for Spherical k-Means Problem with Penalties Using Local Search Techniques

Author

Listed:
  • Xiaoyun Tian

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

  • Ling Gai

    (Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, P. R. China)

  • Yicheng Xu

    (Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, P. R. China)

  • Dongmei Zhang

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

Abstract

In this paper, we consider the spherical k-means problem with penalties, a robust model of spherical clusterings that requires identifying outliers during clustering to improve the quality of the solution. Each outlier will incur a specified penalty cost. In this problem, one should detect the outliers and propose a k-clustering for the given data set so as to minimize the sum of the clustering and penalty costs. As our main contribution, we present a (16 + 83)-approximation via single-swap local search and an (8 + 27 + 𠜀)-approximation via multi-swap local search.

Suggested Citation

  • Xiaoyun Tian & Ling Gai & Yicheng Xu & Dongmei Zhang, 2023. "Approximation Algorithms for Spherical k-Means Problem with Penalties Using Local Search Techniques," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(01), pages 1-16, February.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:01:n:s0217595922400140
    DOI: 10.1142/S0217595922400140
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