An approximation algorithm for the spherical k-means problem with outliers by local search

Yishui Wang (), Chenchen Wu (), Dongmei Zhang () and Juan Zou ()
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Yishui Wang: University of Science and Technology Beijing
Chenchen Wu: Tianjin University of Technology
Dongmei Zhang: Shandong Jianzhu University
Juan Zou: Qufu Normal University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 4, No 14, 2410-2422

Abstract: 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.

Keywords: Spherical k-means; Outliers; Approximation algorithm; Local search (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00734-0

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