k-means clustering of extremes

Anja Janßen, Phyllis Wan

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1211-1233
Number of pages23
JournalElectronic Journal of Statistics
Volume14
Issue number1
DOIs
StatePublished - Jan 1 2020

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Keywords

  • Dimension reduction
  • Extreme value statistics
  • K-means clustering
  • Spectral measure

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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