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The spherical k-means++ algorithm via local search scheme

Author

Listed:
  • Xiaoyun Tian

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Donglei Du

    (University of New Brunswick)

  • Ling Gai

    (Donghua University)

Abstract

The spherical k-means problem (SKMP) is an important variant of the k-means clustering problem (KMP). In this paper, we consider the SKMP, which aims to divide the n points in a given data point set $${\mathcal {S}}$$ S into k clusters so as to minimize the total sum of the cosine dissimilarity measure from each data point to their respective closest cluster center. Our main contribution is to design an expected constant approximation algorithm for the SKMP by integrating the seeding algorithm for the KMP and the local search technique. By utilizing the structure of the clusters, we further obtain an improved LocalSearch++ algorithm involving $$\varepsilon k$$ ε k local search steps.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-021-00737-x
    DOI: 10.1007/s10878-021-00737-x
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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).
    3. 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.
    4. 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.
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