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Significance testing in clustering. (English) Zbl 1396.62141

Hennig, Christian (ed.) et al., Handbook of cluster analysis. Boca Raton, FL: CRC Press (ISBN 978-1-4665-5188-6/hbk; 978-1-4665-5189-3/ebook). Chapman & Hall/CRC Handbooks of Modern Statistical Methods, 315-335 (2016).
Summary: In this chapter, we give an overview of principles and ideas for significance testing in cluster analysis. We review test statistics and null models proposed in the literature and discuss issues such as parametric bootstrap, estimating the number of clusters by use of significance tests and p-values for single clusters.
Then, we focus on the statistical significance of clustering (SigClust) method which is a recently developed cluster evaluation tool specifically designed for testing clustering results for high-dimensional low sample size data. SigClust assesses the significance of departures from a Gaussian null distribution, using invariance properties to reduce the needed parameter estimation. We illustrate the basic idea and implementation of SigClust and give examples.
For the entire collection see [Zbl 1331.68001].

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H15 Hypothesis testing in multivariate analysis
62F40 Bootstrap, jackknife and other resampling methods

Software:

SigClust
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