  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.
