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The seeding algorithms for spherical k-means clustering

Author

Listed:
  • Min Li

    (Shandong Normal University)

  • Dachuan Xu

    (Beijing University of Technology)

  • Dongmei Zhang

    (Shandong Jianzhu University)

  • Juan Zou

    (Qufu Normal University)

Abstract

In order to cluster the textual data with high dimension in modern data analysis, the spherical k-means clustering is presented. It aims to partition the given points with unit length into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In this paper, we mainly study seeding algorithms for spherical k-means clustering, for its special case (with separable sets), as well as for its generalized problem ($$\alpha $$α-spherical k-means clustering). About the spherical k-means clustering with separable sets, an approximate algorithm with a constant factor is presented. Moreover, it can be generalized to the $$\alpha $$α-spherical separable k-means clustering. By slickly constructing a useful function, we also show that the famous seeding algorithms such as k-means++ and k-means|| for k-means problem can be applied directly to solve the $$\alpha $$α-spherical k-means clustering. Except for theoretical analysis, the numerical experiment is also included.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00779-w
    DOI: 10.1007/s10898-019-00779-w
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. 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.
    2. Quanmin Guo & Jiahao Liang & Hanlei Wang, 2023. "Night Vision Anti-Halation Algorithm of Different-Source Image Fusion Based on Low-Frequency Sequence Generation," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
    3. Jinqi Su & Changhong Dong & Ke Su & Lin He, 2023. "Research on the Construction of Digital Economy Index System Based on K-means-SA Algorithm," SAGE Open, , vol. 13(4), pages 21582440231, December.
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    5. 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.
    6. Peipei You & Sitao Li & Chengren Li & Chao Zhang & Hailang Zhou & Huicai Wang & Huiru Zhao & Yihang Zhao, 2023. "Price-Based Demand Response: A Three-Stage Monthly Time-of-Use Tariff Optimization Model," Energies, MDPI, vol. 16(23), pages 1-20, November.

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