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The seeding algorithms for spherical k-means clustering

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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 (\(\alpha \)-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 \(\alpha \)-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 \(\alpha \)-spherical k-means clustering. Except for theoretical analysis, the numerical experiment is also included.

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Acknowledgements

The first author is supported by the Higher Educational Science and Technology Program of Shandong Province (No. J17KA171). The second author is supported by Natural Science Foundation of China (No. 11531014). The third author is supported by Natural Science Foundation of China (No. 11871081). The fourth author is supported by Natural Science Foundation of China (No. 11801310).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P.R. China

    Min Li

  2. Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, 100124, P.R. China

    Dachuan Xu

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

    Dongmei Zhang

  4. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P.R. China

    Juan Zou

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  1. Min Li
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  2. Dachuan Xu
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  3. Dongmei Zhang
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  4. Juan Zou
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Correspondence to Dongmei Zhang.

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Li, M., Xu, D., Zhang, D. et al. The seeding algorithms for spherical k-means clustering. J Glob Optim 76, 695–708 (2020). https://doi.org/10.1007/s10898-019-00779-w

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