Abstract
In this paper, we study the spherical k-means problem (SKMP) which is one of the most well-studied clustering problems. In the SKMP, we are given an n-client set \( \mathcal {D}\) in d-dimensional unit sphere \(\mathbb {S}^d\), and an integer \(k \le n\). The goal is to open a center subset \(F \subset \mathbb {S}^d\) with \( |F| \le k\) that minimizes the sum of cosine dissimilarity measure for each client in \( \mathcal {D} \) to the nearest open center. We give a \((2 (4+\sqrt{7}) + \varepsilon )\)-approximation algorithm for this problem using local search scheme.
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Acknowledgements
The first author is supported by Natural Science Foundation of China (No. 11871081). The second author is supported by Natural Science Foundation of China (No. 11871366). The third author is the Higher Educational Science and Technology Program of Shandong Province (No. J17KA171). The fourth author is supported by Natural Science Foundation of China (No. 61433012), Shenzhen Research Grant (KQJSCX2018033017 0311901, JCYJ20180305180840138 and GFW2017073114031767), and Hong Kong GRF 17210017. The fifth author is supported by Natural Science Foundation of China (No. 11531014).
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Zhang, D., Cheng, Y., Li, M., Wang, Y., Xu, D. (2019). Local Search Approximation Algorithms for the Spherical k-Means Problem. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_31
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DOI: https://doi.org/10.1007/978-3-030-27195-4_31
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