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The seeding algorithm for spherical k-means clustering with penalties

Author

Listed:
  • Sai Ji

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Longkun Guo

    (Qilu University of Technology (Shandong Academy of Sciences))

  • Min Li

    (Shandong Normal University)

  • Dongmei Zhang

    (Shandong Jianzhu University)

Abstract

Spherical k-means clustering as a known NP-hard variant of the k-means problem has broad applications in data mining. In contrast to k-means, it aims to partition a collection of given data distributed on a spherical surface into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In the paper, we introduce spherical k-means clustering with penalties and give a $$2\max \{2,M\}(1+M)(\ln k+2)$$ 2 max { 2 , M } ( 1 + M ) ( ln k + 2 ) -approximation algorithm. Moreover, we prove that when against spherical k-means clustering with penalties but on separable instances, our algorithm is with an approximation ratio $$2\max \{3,M+1\}$$ 2 max { 3 , M + 1 } with high probability, where M is the ratio of the maximal and the minimal penalty cost of the given data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00569-1
    DOI: 10.1007/s10878-020-00569-1
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    References listed on IDEAS

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    1. 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.
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