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An approximation algorithm for the spherical k-means problem with outliers by local search

Author

Listed:
  • Yishui Wang

    (University of Science and Technology Beijing)

  • Chenchen Wu

    (Tianjin University of Technology)

  • Dongmei Zhang

    (Shandong Jianzhu University)

  • Juan Zou

    (Qufu Normal University)

Abstract

We consider the spherical k-means problem with outliers, an extension of the k-means problem. In this clustering problem, all sample points are on the unit sphere. Given two integers k and z, we can ignore at most z points (outliers) and need to find at most k cluster centers on the unit sphere and assign remaining points to these centers to minimize the k-means objective. It has been proved that any algorithm with a bounded approximation ratio cannot return a feasible solution for this problem. Our contribution is to present a local search bi-criteria approximation algorithm for the spherical k-means problem.

Suggested Citation

  • Yishui Wang & Chenchen Wu & Dongmei Zhang & Juan Zou, 2022. "An approximation algorithm for the spherical k-means problem with outliers by local search," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2410-2422, November.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-021-00734-0
    DOI: 10.1007/s10878-021-00734-0
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    References listed on IDEAS

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    1. Min Li & Dachuan Xu & Dongmei Zhang & Juan Zou, 2020. "The seeding algorithms for spherical k-means clustering," Journal of Global Optimization, Springer, vol. 76(4), pages 695-708, April.
    2. Hornik, Kurt & Feinerer, Ingo & Kober, Martin & Buchta, Christian, 2012. "Spherical k-Means Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i10).
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