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Selection of the number of clusters via the bootstrap method

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  • Fang, Yixin
  • Wang, Junhui

Abstract

Here the problem of selecting the number of clusters in cluster analysis is considered. Recently, the concept of clustering stability, which measures the robustness of any given clustering algorithm, has been utilized in Wang (2010) for selecting the number of clusters through cross validation. In this paper, an estimation scheme for clustering instability is developed based on the bootstrap, and then the number of clusters is selected so that the corresponding estimated clustering instability is minimized. The proposed selection criterion’s effectiveness is demonstrated on simulations and real examples.

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  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:468-477
    DOI: 10.1016/j.csda.2011.09.003
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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.
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    3. Fang, Yixin & Wang, Junhui, 2011. "Penalized cluster analysis with applications to family data," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2128-2136, June.
    4. Witten, Daniela M. & Tibshirani, Robert, 2010. "A Framework for Feature Selection in Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 713-726.
    5. 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.
    6. 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.
    7. Abba Krieger & Paul Green, 1999. "A cautionary note on using internal cross validation to select the number of clusters," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 341-353, September.
    8. Junhui Wang, 2010. "Consistent selection of the number of clusters via crossvalidation," Biometrika, Biometrika Trust, vol. 97(4), pages 893-904.
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    Citations

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    Cited by:

    1. Han Yu & Brian Chapman & Arianna Di Florio & Ellen Eischen & David Gotz & Mathews Jacob & Rachael Hageman Blair, 2019. "Bootstrapping estimates of stability for clusters, observations and model selection," Computational Statistics, Springer, vol. 34(1), pages 349-372, March.
    2. 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.
    3. 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.
    4. Peter Radchenko & Gourab Mukherjee, 2017. "Convex clustering via l 1 fusion penalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1527-1546, November.
    5. Rozmus Dorota, 2020. "Clustering Poland Among Eu Countries in Terms of a Sustainable Development Level in the Light of Various Cluster Stability Measures," Folia Oeconomica Stetinensia, Sciendo, vol. 20(1), pages 319-340, June.
    6. Binhuan Wang & Lanqiu Yao & Jiyuan Hu & Huilin Li, 2023. "A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 193-216, April.
    7. Erika S. Helgeson & David M. Vock & Eric Bair, 2021. "Nonparametric cluster significance testing with reference to a unimodal null distribution," Biometrics, The International Biometric Society, vol. 77(4), pages 1215-1226, December.
    8. Damien Jourdain & Juliette Lairez & Bruno Striffler & François Affholder, 2020. "Farmers’ preference for cropping systems and the development of sustainable intensification: a choice experiment approach," Review of Agricultural, Food and Environmental Studies, Springer, vol. 101(4), pages 417-437, December.
    9. Vincent Audigier & Ndèye Niang, 2023. "Clustering with missing data: which equivalent for Rubin’s rules?," 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. 17(3), pages 623-657, September.
    10. Jourdain, Damien & Lairez, Juliette & Striffler, Bruno & Affholder, François, 2020. "Farmers’ preference for cropping systems and the development of sustainable intensification: a choice experiment approach," Review of Agricultural, Food and Environmental Studies, Institut National de la Recherche Agronomique (INRA), vol. 101(4), March.
    11. Coraggio, Luca & Coretto, Pietro, 2023. "Selecting the number of clusters, clustering models, and algorithms. A unifying approach based on the quadratic discriminant score," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    12. Yujia Li & Xiangrui Zeng & Chien‐Wei Lin & George C. Tseng, 2022. "Simultaneous estimation of cluster number and feature sparsity in high‐dimensional cluster analysis," Biometrics, The International Biometric Society, vol. 78(2), pages 574-585, June.
    13. Damien Jourdain & Juliette Lairez & Bruno Striffler & François Affholder, 2020. "Farmers’ preference for cropping systems and the development of sustainable intensification: a choice experiment approach," Post-Print hal-02995632, HAL.
    14. Damien Jourdain1,2,3 & Juliette Lairez4,5 & Bruno Striffler & François Affholder, 2020. "Farmers’ preference for cropping systems and the development of sustainable intensification: a choice experiment approach," Review of Agricultural, Food and Environmental Studies, INRA Department of Economics, vol. 101(4), pages 417-437.
    15. ADACHI Daisuke & FUKAI Taiyo & KAWAGUCHI Daiji & SAITO Yukiko, 2020. "Commuting Zones in Japan," Discussion papers 20021, Research Institute of Economy, Trade and Industry (RIETI).

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