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.

翻译：条件极值（CE）框架已被证明在分析随机向量的联合尾部行为方面具有重要价值。然而，当将其应用于多个位置或变量时，所得极值相依结构往往难以解释或比较，尤其对于高维向量而言。为解决这一问题，我们提出了一种基于CE框架的多元极值聚类新方法。该方法基于偏斜几何Jensen-Shannon散度，引入了一种闭式、计算高效的多元尾部相异性度量，适用于任意维度。通过将标准聚类算法应用于成对距离矩阵，我们获得了具有同质尾部相依性的可解释随机向量组。模拟研究表明，我们的方法在二元极值聚类方面优于现有方法，并能独特地扩展到多元场景。在爱尔兰气象数据的应用中，我们的聚类方法识别出了具有相似降水与风速极值相依性的空间连贯区域。