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A non-parametric method to estimate the number of clusters

Author

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  • Fujita, André
  • Takahashi, Daniel Y.
  • Patriota, Alexandre G.

Abstract

An important and yet unsolved problem in unsupervised data clustering is how to determine the number of clusters. The proposed slope statistic is a non-parametric and data driven approach for estimating the number of clusters in a dataset. This technique uses the output of any clustering algorithm and identifies the maximum number of groups that breaks down the structure of the dataset. Intensive Monte Carlo simulation studies show that the slope statistic outperforms (for the considered examples) some popular methods that have been proposed in the literature. Applications in graph clustering, in iris and breast cancer datasets are shown.

Suggested Citation

  • Fujita, André & Takahashi, Daniel Y. & Patriota, Alexandre G., 2014. "A non-parametric method to estimate the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 27-39.
    • Handle: RePEc:eee:csdana:v:73:y:2014:i:c:p:27-39
    DOI: 10.1016/j.csda.2013.11.012
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    References listed on IDEAS

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    1. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. Sugar, Catherine A. & James, Gareth M., 2003. "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 750-763, January.
    4. Fang, Yixin & Wang, Junhui, 2012. "Selection of the number of clusters via the bootstrap method," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 468-477.
    5. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
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    Cited by:

    1. Jonas M. B. Haslbeck & Dirk U. Wulff, 2020. "Estimating the number of clusters via a corrected clustering instability," Computational Statistics, Springer, vol. 35(4), pages 1879-1894, December.
    2. Koltcov, Sergei, 2018. "Application of Rényi and Tsallis entropies to topic modeling optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1192-1204.
    3. Fujita, André & Takahashi, Daniel Yasumasa & Balardin, Joana Bisol & Vidal, Maciel Calebe & Sato, João Ricardo, 2017. "Correlation between graphs with an application to brain network analysis," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 76-92.

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