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Consistent selection of the number of clusters via crossvalidation

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  • Junhui Wang

Abstract

In cluster analysis, one of the major challenges is to estimate the number of clusters. Most existing approaches attempt to minimize some distance-based dissimilarity measure within clusters. This article proposes a novel selection criterion that is applicable to all kinds of clustering algorithms, including distance based or non-distance based algorithms. The key idea is to select the number of clusters that minimizes the algorithm's instability, which measures the robustness of any given clustering algorithm against the randomness in sampling.Anovel estimation scheme for clustering instability is developed based on crossvalidation. The proposed selection criterion's effectiveness is demonstrated on a variety of numerical experiments, and its asymptotic selection consistency is established when the dataset is properly split. Copyright 2010, Oxford University Press.

Suggested Citation

  • Junhui Wang, 2010. "Consistent selection of the number of clusters via crossvalidation," Biometrika, Biometrika Trust, vol. 97(4), pages 893-904.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:893-904
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    File URL: http://hdl.handle.net/10.1093/biomet/asq061
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    1. repec:bla:jorssb:v:79:y:2017:i:5:p:1527-1546 is not listed on IDEAS
    2. Wang, Junhui & Fang, Yixin, 2013. "Analysis of presence-only data via semi-supervised learning approaches," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 134-143.
    3. 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.
    4. Yoshikazu Terada, 2014. "Strong Consistency of Reduced K-means Clustering," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 913-931, December.

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