Clustering of multivariate tail dependence using conditional methods

TL;DR

This paper introduces a new clustering method for multivariate tail dependence based on the conditional extremes framework, providing interpretable groups and improved performance in high-dimensional extremal dependence analysis.

Contribution

The paper proposes a novel, computationally efficient dissimilarity measure for multivariate tails and applies standard clustering algorithms to identify homogeneous extremal dependence groups.

Findings

Method outperforms existing approaches in bivariate extremes clustering.

Extends to multivariate settings, capturing complex tail dependence structures.

Identifies spatially coherent regions in meteorological data.

Abstract

The conditional extremes (CE) framework has proven useful for analysing the joint tail behaviour of random vectors. However, when applied across many locations or variables, it can be difficult to interpret or compare the resulting extremal dependence structures, particularly for high dimensional vectors. To address this, we propose a novel clustering method for multivariate extremes using the CE framework. Our approach introduces a closed-form, computationally efficient dissimilarity measure for multivariate tails, based on the skew-geometric Jensen-Shannon divergence, and is applicable in arbitrary dimensions. Applying standard clustering algorithms to a matrix of pairwise distances, we obtain interpretable groups of random vectors with homogeneous tail dependence. Simulation studies demonstrate that our method outperforms existing approaches for clustering bivariate extremes, and uniquely extends to the multivariate setting. In our application to Irish meteorological data, our clustering identifies spatially coherent regions with similar extremal dependence between precipitation and wind speeds.