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2020 $k$-means clustering of extremes
Anja Janßen, Phyllis Wan
Electron. J. Statist. 14(1): 1211-1233 (2020). DOI: 10.1214/20-EJS1689


The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means algorithm can be applied in the analysis of only the extremal observations from a data set. By making use of multivariate extreme value analysis we show how it can be adopted to find “prototypes” of extremal dependence and derive a consistency result for our suggested estimator. In the special case of max-linear models we show furthermore that our procedure provides an alternative way of statistical inference for this class of models. Finally, we provide data examples which show that our method is able to find relevant patterns in extremal observations and allows us to classify extremal events.


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Anja Janßen. Phyllis Wan. "$k$-means clustering of extremes." Electron. J. Statist. 14 (1) 1211 - 1233, 2020.


Received: 1 May 2019; Published: 2020
First available in Project Euclid: 3 March 2020

zbMATH: 07200227
MathSciNet: MR4071364
Digital Object Identifier: 10.1214/20-EJS1689

Primary: 62G32
Secondary: 62H30, 60G70

Keywords: $k$-means clustering , Dimension reduction , Extreme value statistics , spectral measure


Vol.14 • No. 1 • 2020
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