The seeding algorithm for spherical k-means clustering with penalties

Sai Ji (), Dachuan Xu (), Longkun Guo (), Min Li () and Dongmei Zhang ()
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Sai Ji: Beijing University of Technology
Dachuan Xu: Beijing University of Technology
Longkun Guo: Qilu University of Technology (Shandong Academy of Sciences)
Min Li: Shandong Normal University
Dongmei Zhang: Shandong Jianzhu University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 3, No 32, 1977-1994

Abstract: Abstract Spherical k-means clustering as a known NP-hard variant of the k-means problem has broad applications in data mining. In contrast to k-means, it aims to partition a collection of given data distributed on a spherical surface into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In the paper, we introduce spherical k-means clustering with penalties and give a $$2\max \{2,M\}(1+M)(\ln k+2)$$ 2 max { 2 , M } ( 1 + M ) ( ln k + 2 ) -approximation algorithm. Moreover, we prove that when against spherical k-means clustering with penalties but on separable instances, our algorithm is with an approximation ratio $$2\max \{3,M+1\}$$ 2 max { 3 , M + 1 } with high probability, where M is the ratio of the maximal and the minimal penalty cost of the given data set.

Keywords: Approximation algorithm; Spherical k-means clustering; Penalty (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-020-00569-1

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