Feature Clustering for Support Identification in Extreme Regions

TL;DR

This paper introduces a new optimization-based method for identifying feature clusters that characterize the dependence structure of multivariate extremes, aiding in risk analysis and anomaly detection.

Contribution

It proposes a novel dimension reduction technique for support identification in extreme regions within the framework of multivariate Extreme Value Theory.

Findings

Effective feature clustering for extreme dependence structures

Improved anomaly detection in multivariate extreme data

Strong empirical validation through numerical experiments

Abstract

Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common characterization of extremes' dependence structure is the angular measure. It is a suitable measure to work in extreme regions as it provides meaningful insights concerning the subregions where extremes tend to concentrate their mass. The present paper develops a novel optimization-based approach to assess the dependence structure of extremes. This support identification scheme rewrites as estimating clusters of features which best capture the support of extremes. The dimension reduction technique we provide is applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.