Abstract
We consider the spherical k-means problem (SKMP), a generalization of the k-means clustering problem (KMP). Given a data set of n points \({\mathcal {P}}\) in d-dimensional unit sphere \({\mathbb {R}}^d\), and an integer \(k \le n\), it aims to partition the data set \({\mathcal {P}}\) into k sets so as to minimize the sum of cosine dissimilarity measure from each data point to its closest center. We present a constant expected approximation guarantee for this problem based on integrating the k-means++ seeding algorithm for the KMP and the local search technique.
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Acknowledgements
The first two authors are supported by National Natural Science Foundation of China (Nos. 11871081, 11531014). 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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Tian, X., Xu, D., Du, D., Gai, L. (2020). The Spherical k-means++ Algorithm via Local Search. In: Zhang, Z., Li, W., Du, DZ. (eds) Algorithmic Aspects in Information and Management. AAIM 2020. Lecture Notes in Computer Science(), vol 12290. Springer, Cham. https://doi.org/10.1007/978-3-030-57602-8_12
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DOI: https://doi.org/10.1007/978-3-030-57602-8_12
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