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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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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DOI: https://doi.org/10.1007/s10878-021-00734-0