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Bootstrapping for Significance of Compact Clusters in Multidimensional Datasets

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  • Ranjan Maitra
  • Volodymyr Melnykov
  • Soumendra N. Lahiri

Abstract

This article proposes a bootstrap approach for assessing significance in the clustering of multidimensional datasets. The procedure compares two models and declares the more complicated model a better candidate if there is significant evidence in its favor. The performance of the procedure is illustrated on two well-known classification datasets and comprehensively evaluated in terms of its ability to estimate the number of components via extensive simulation studies, with excellent results. The methodology is also applied to the problem of k -means color quantization of several standard images in the literature and is demonstrated to be a viable approach for determining the minimal and optimal numbers of colors needed to display an image without significant loss in resolution. Additional illustrations and performance evaluations are provided in the online supplementary material.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:378-392 DOI: 10.1080/01621459.2011.646935
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    Cited by:

    1. 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.

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