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

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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.

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Acknowledgements

The first author is funded by NSFC (No. 12001039) and the Fundamental Research Funds for the Central Universities, USTB (FRF-TP-20-074A1). The second author is funded by NSFC (No. 11971349). The third author is funded by NSFC (No. 11871081). The fourth author is funded by NSFC (No. 11801310).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, P.R. China

    Yishui Wang

  2. College of Science, Tianjin University of Technology, Tianjin, 300384, P.R. China

    Chenchen Wu

  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. Yishui Wang
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  2. Chenchen Wu
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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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A preliminary version of this paper appeared in Proceedings of the 14th International Conference on Algorithmic Applications in Management, pp 141-148, 2020.

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Wang, Y., Wu, C., Zhang, D. et al. An approximation algorithm for the spherical k-means problem with outliers by local search. J Comb Optim 44, 2410–2422 (2022). https://doi.org/10.1007/s10878-021-00734-0

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