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 \({\mathcal {S}}\) 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 \(\varepsilon k\) local search steps.
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Acknowledgements
The first two authors are supported by National Natural Science Foundation of China (No. 11871081) and Beijing Natural Science Foundation Project No. Z200002. The third author is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 06446, and National Natural Science Foundation of China (Nos. 11771386, 11728104). The fourth author is supported by National Natural Science Foundation of China (No. 11201333).
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A preliminary version of this paper appeared in Proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management, pp. 131–140, 2020.
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Tian, X., Xu, D., Du, D. et al. The spherical k-means++ algorithm via local search scheme. J Comb Optim 44, 2375–2394 (2022). https://doi.org/10.1007/s10878-021-00737-x
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DOI: https://doi.org/10.1007/s10878-021-00737-x