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Spherical k-Means Clustering

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  • Hornik, Kurt
  • Feinerer, Ingo
  • Kober, Martin
  • Buchta, Christian

Abstract

Clustering text documents is a fundamental task in modern data analysis, requiring approaches which perform well both in terms of solution quality and computational efficiency. Spherical k-means clustering is one approach to address both issues, employing cosine dissimilarities to perform prototype-based partitioning of term weight representations of the documents. This paper presents the theory underlying the standard spherical k-means problem and suitable extensions, and introduces the R extension package skmeans which provides a computational environment for spherical k-means clustering featuring several solvers: a fixed-point and genetic algorithm, and interfaces to two external solvers (CLUTO and Gmeans). Performance of these solvers is investigated by means of a large scale benchmark experiment.

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  • Hornik, Kurt & Feinerer, Ingo & Kober, Martin & Buchta, Christian, 2012. "Spherical k-Means Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i10).
    • Handle: RePEc:jss:jstsof:v:050:i10
    DOI: http://hdl.handle.net/10.18637/jss.v050.i10
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    References listed on IDEAS

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    1. Feinerer, Ingo & Hornik, Kurt & Meyer, David, 2008. "Text Mining Infrastructure in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i05).
    2. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    3. Hornik, Kurt, 2005. "A CLUE for CLUster Ensembles," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i12).
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    Cited by:

    1. Yishui Wang & Chenchen Wu & Dongmei Zhang & Juan Zou, 2022. "An approximation algorithm for the spherical k-means problem with outliers by local search," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2410-2422, November.
    2. Swapnajit Chakraborti & Shubhamoy Dey, 2019. "Analysis of Competitor Intelligence in the Era of Big Data: An Integrated System Using Text Summarization Based on Global Optimization," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 61(3), pages 345-355, June.
    3. Francesco Trebbi & Eric Weese, 2019. "Insurgency and Small Wars: Estimation of Unobserved Coalition Structures," Econometrica, Econometric Society, vol. 87(2), pages 463-496, March.
    4. Adelaide Figueiredo, 2017. "Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 39-52, December.
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    7. Lüdering Jochen & Winker Peter, 2016. "Forward or Backward Looking? The Economic Discourse and the Observed Reality," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(4), pages 483-515, August.
    8. Kirschstein, Thomas & Liebscher, Steffen & Pandolfo, Giuseppe & Porzio, Giovanni C. & Ragozini, Giancarlo, 2019. "On finite-sample robustness of directional location estimators," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 53-75.
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    10. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    11. Sergio Bolívar & Alicia Nieto-Reyes & Heather L. Rogers, 2023. "Statistical Depth for Text Data: An Application to the Classification of Healthcare Data," Mathematics, MDPI, vol. 11(1), pages 1-20, January.
    12. Diana Purwitasari & Chastine Fatichah & Surya Sumpeno & Christian Steglich & Mauridhi Hery Purnomo, 2020. "Identifying collaboration dynamics of bipartite author-topic networks with the influences of interest changes," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(3), pages 1407-1443, March.
    13. Min Li & Dachuan Xu & Dongmei Zhang & Juan Zou, 2020. "The seeding algorithms for spherical k-means clustering," Journal of Global Optimization, Springer, vol. 76(4), pages 695-708, April.
    14. Lazar, Drew & Lin, Lizhen, 2017. "Scale and curvature effects in principal geodesic analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 64-82.
    15. repec:kob:wpaper:1628 is not listed on IDEAS
    16. Xiaoyun Tian & Dachuan Xu & Donglei Du & Ling Gai, 2022. "The spherical k-means++ algorithm via local search scheme," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2375-2394, November.
    17. Xavier Bry & Lionel Cucala, 2022. "A von Mises–Fisher mixture model for clustering numerical and categorical variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 429-455, June.
    18. Dong, Aqi & Melnykov, Volodymyr, 2024. "Contaminated Kent mixture model for clustering non-spherical directional data with heavy tails or scatter," Statistics & Probability Letters, Elsevier, vol. 208(C).

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