The seeding algorithms for spherical k-means clustering

Min Li, Dachuan Xu, Dongmei Zhang () and Juan Zou
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Min Li: Shandong Normal University
Dachuan Xu: Beijing University of Technology
Dongmei Zhang: Shandong Jianzhu University
Juan Zou: Qufu Normal University

Journal of Global Optimization, 2020, vol. 76, issue 4, No 3, 695-708

Abstract: Abstract In order to cluster the textual data with high dimension in modern data analysis, the spherical k-means clustering is presented. It aims to partition the given points with unit length into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In this paper, we mainly study seeding algorithms for spherical k-means clustering, for its special case (with separable sets), as well as for its generalized problem ($$\alpha $$α-spherical k-means clustering). About the spherical k-means clustering with separable sets, an approximate algorithm with a constant factor is presented. Moreover, it can be generalized to the $$\alpha $$α-spherical separable k-means clustering. By slickly constructing a useful function, we also show that the famous seeding algorithms such as k-means++ and k-means|| for k-means problem can be applied directly to solve the $$\alpha $$α-spherical k-means clustering. Except for theoretical analysis, the numerical experiment is also included.

Keywords: Approximation algorithm; Spherical k-means clustering; k-means problem; Separable set; Seeding algorithm (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10898-019-00779-w

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