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The bi-criteria seeding algorithms for two variants of k-means problem

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Abstract

The k-means problem is very classic and important in computer science and machine learning, so there are many variants presented depending on different backgrounds, such as the k-means problem with penalties, the spherical k-means clustering, and so on. Since the k-means problem is NP-hard, the research of its approximation algorithm is very hot. In this paper, we apply a bi-criteria seeding algorithm to both k-means problem with penalties and spherical k-means problem, and improve (upon) the performance guarantees given by the k-means++ algorithm for these two problems.

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Acknowledgements

The author is supported by Higher Educational Science and Technology Program of Shandong Province (No. J17KA171) and Shandong Provincial Natural Science Foundation (No. ZR2019MA032) of China.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Min Li

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  1. Min Li
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Correspondence to Min Li.

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Dedicated to Professor Minyi Yue on the Occasion of His 100th Birthday.

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Li, M. The bi-criteria seeding algorithms for two variants of k-means problem. J Comb Optim 44, 1693–1704 (2022). https://doi.org/10.1007/s10878-020-00537-9

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