Clustering of multivariate tail dependence using conditional methods

2025-10-23

AI Summary

Interpreting and comparing tail dependence structures across variables or spatial locations in high-dimensional random vectors remains challenging. To address this, we propose a novel clustering framework grounded in the conditional extremes (CE) paradigm. Our key contribution is the development of the first closed-form, dimension-agnostic tail dissimilarity measure—the partial geometric Jensen–Shannon divergence—which generalizes beyond pairwise dependence to enable interpretable grouping of multivariate extremal dependence patterns. Integrated with standard clustering algorithms via pairwise distance matrices, our approach ensures computational efficiency, spatial interpretability, and scalability. In simulation studies, it substantially outperforms existing bivariate clustering methods. Applied to Irish meteorological data, it successfully identifies spatially coherent regions exhibiting similar extremal dependence between precipitation and wind speed.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Clustering multivariate extremes using conditional methods
• Developing efficient dissimilarity measure for tail dependence
• Identifying homogeneous extremal dependence structures in high dimensions

Innovation

• Clustering multivariate extremes using conditional extremes framework
• Introducing skew-geometric Jensen-Shannon divergence dissimilarity measure
• Applying standard algorithms to pairwise distances for grouping