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On the Added Value of Bootstrap Analysis for K-Means Clustering

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  • Joeri Hofmans
  • Eva Ceulemans
  • Douglas Steinley
  • Iven Mechelen

Abstract

Because of its deterministic nature, K-means does not yield confidence information about centroids and estimated cluster memberships, although this could be useful for inferential purposes. In this paper we propose to arrive at such information by means of a non-parametric bootstrap procedure, the performance of which is tested in an extensive simulation study. Results show that the coverage of hyper-ellipsoid bootstrap confidence regions for the centroids is in general close to the nominal coverage probability. For the cluster memberships, we found that probabilistic membership information derived from the bootstrap analysis can be used to improve the cluster assignment of individual objects, albeit only in the case of a very large number of clusters. However, in the case of smaller numbers of clusters, the probabilistic membership information still appeared to be useful as it indicates for which objects the cluster assignment resulting from the analysis of the original data is likely to be correct; hence, this information can be used to construct a partial clustering in which the latter objects only are assigned to clusters. Copyright Classification Society of North America 2015

Suggested Citation

  • Joeri Hofmans & Eva Ceulemans & Douglas Steinley & Iven Mechelen, 2015. "On the Added Value of Bootstrap Analysis for K-Means Clustering," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 268-284, July.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:2:p:268-284
    DOI: 10.1007/s00357-015-9178-y
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    References listed on IDEAS

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    1. Hand, David J. & Krzanowski, Wojtek J., 2005. "Optimising k-means clustering results with standard software packages," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 969-973, June.
    2. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    3. Hennig, Christian, 2007. "Cluster-wise assessment of cluster stability," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 258-271, September.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    5. Glenn Milligan, 1985. "An algorithm for generating artificial test clusters," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 123-127, March.
    6. Ranjan Maitra & Volodymyr Melnykov & Soumendra N. Lahiri, 2012. "Bootstrapping for Significance of Compact Clusters in Multidimensional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 378-392, March.
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    Cited by:

    1. Daniel Aloise & Nielsen Castelo Damasceno & Nenad Mladenović & Daniel Nobre Pinheiro, 2017. "On Strategies to Fix Degenerate k-means Solutions," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 165-190, July.
    2. Lauri Varmann & Helena Mouriño, 2024. "Clustering Empirical Bootstrap Distribution Functions Parametrized by Galton–Watson Branching Processes," Mathematics, MDPI, vol. 12(15), pages 1-25, August.
    3. Aurora Torrente & Juan Romo, 2021. "Initializing k-means Clustering by Bootstrap and Data Depth," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 232-256, July.

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