Bootstrapping for Significance of Compact Clusters in Multidimensional Datasets

Date
2012-01-30
Authors
Maitra, Ranjan
Melnykov, Volodymyr
Lahiri, Soumendra
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Altmetrics
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Statistics
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Statistics
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.

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This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on January 30, 2012, available online: http://www.tandf.com/10.1080/01621459.2011.646935.

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