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Bootstrapping estimates of stability for clusters, observations and model selection

Author

Listed:
  • Han Yu

    (State University of New York at Buffalo)

  • Brian Chapman

    (University of Utah)

  • Arianna Di Florio

    (Cardiff University School of Medicine
    University of North Carolina at Chapel Hill)

  • Ellen Eischen

    (University of Oregon)

  • David Gotz

    (University of North Carolina at Chapel Hill)

  • Mathews Jacob

    (University of Iowa)

  • Rachael Hageman Blair

    (State University of New York at Buffalo)

Abstract

Clustering is a challenging problem in unsupervised learning. In lieu of a gold standard, stability has become a valuable surrogate to performance and robustness. In this work, we propose a non-parametric bootstrapping approach to estimating the stability of a clustering method, which also captures stability of the individual clusters and observations. This flexible framework enables different types of comparisons between clusterings and can be used in connection with two possible bootstrap approaches for stability. The first approach, scheme 1, can be used to assess confidence (stability) around clustering from the original dataset based on bootstrap replications. A second approach, scheme 2, searches over the bootstrap clusterings for an optimally stable partitioning of the data. The two schemes accommodate different model assumptions that can be motivated by an investigator’s trust (or lack thereof) in the original data and additional computational considerations. We propose a hierarchical visualization extrapolated from the stability profiles that give insights into the separation of groups, and projected visualizations for the inspection of the stability of individual operations. Our approaches show good performance in simulation and on real data. These approaches can be implemented using the R package bootcluster that is available on the Comprehensive R Archive Network (CRAN).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0830-y
    DOI: 10.1007/s00180-018-0830-y
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    References listed on IDEAS

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    1. Junhui Wang, 2010. "Consistent selection of the number of clusters via crossvalidation," Biometrika, Biometrika Trust, vol. 97(4), pages 893-904.
    2. Hennig, Christian, 2007. "Cluster-wise assessment of cluster stability," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 258-271, September.
    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.
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