The spherical k-means++ algorithm via local search scheme

Xiaoyun Tian (), Dachuan Xu (), Donglei Du () and Ling Gai ()
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Xiaoyun Tian: Beijing University of Technology
Dachuan Xu: Beijing University of Technology
Donglei Du: University of New Brunswick
Ling Gai: Donghua University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 4, No 12, 2375-2394

Abstract: Abstract The spherical k-means problem (SKMP) is an important variant of the k-means clustering problem (KMP). In this paper, we consider the SKMP, which aims to divide the n points in a given data point set $${\mathcal {S}}$$ S into k clusters so as to minimize the total sum of the cosine dissimilarity measure from each data point to their respective closest cluster center. Our main contribution is to design an expected constant approximation algorithm for the SKMP by integrating the seeding algorithm for the KMP and the local search technique. By utilizing the structure of the clusters, we further obtain an improved LocalSearch++ algorithm involving $$\varepsilon k$$ ε k local search steps.

Keywords: Spherical k-means; Local search; Seeding algorithm; Approximation algorithm (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00737-x

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