# k-means clustering of extremes

arXiv: https://arxiv.org/abs/1904.02970 · HTML: https://mlsanity.com/paper/1904.02970/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2019.

## Built on by (most cited first, 11 of 11)

- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)
- [On Regression in Extreme Regions](https://mlsanity.com/paper/2303.03084/) (2023)
- [Spectral learning of multivariate extremes](https://mlsanity.com/paper/2111.07799/) (2021)
- [Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremes](https://mlsanity.com/paper/2308.01023/) (2023)
- [Kernel PCA for multivariate extremes](https://mlsanity.com/paper/2211.13172/) (2022)
- [High-dimensional variable clustering based on maxima of a weakly dependent random process](https://mlsanity.com/paper/2302.00934/) (2023)
- [Simulation of Multivariate Extremes: a Wasserstein-Aitchison GAN approach](https://mlsanity.com/paper/2504.21438/) (2025)
- [Multi-site modelling and reconstruction of past extreme skew surges along the French Atlantic coast](https://mlsanity.com/paper/2505.00835/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Canonical Tail Dependence for Soft Extremal Clustering of Multichannel Brain Signals](https://mlsanity.com/paper/2512.06435/) (2025)
- [Principal Component Analysis for Multivariate Extremes](https://mlsanity.com/paper/2606.07213/) (2026)

## Abstract (arXiv)

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 we 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.