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We propose a spectral clustering algorithm for analyzing the dependencestructure of multivariate extremes. More specifically, we focus on theasymptotic dependence of multivariate extremes characterized by the angular orspectral measure in extreme value theory. Our work studies the theoreticalperformance of spectral clustering based on a random $k$-nearest neighbor graphconstructed from an extremal sample, i.e., the angular part of random vectorsfor which the radius exceeds a large threshold. In particular, we derive theasymptotic distribution of extremes arising from a linear factor model andprove that, under certain conditions, spectral clustering can consistentlyidentify the clusters of extremes arising in this model. Leveraging this resultwe propose a simple consistent estimation strategy for learning the angularmeasure. Our theoretical findings are complemented with numerical experimentsillustrating the finite sample performance of our methods.

Spectral learning of multivariate extremes