Log In Sign Up

Spectral learning of multivariate extremes

by   Marco Avella-Medina, et al.

We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure in extreme value theory. Our work studies the theoretical performance of spectral clustering based on a random k-nearest neighbor graph constructed from an extremal sample, i.e., the angular part of random vectors for which the radius exceeds a large threshold. In particular, we derive the asymptotic distribution of extremes arising from a linear factor model and prove that, under certain conditions, spectral clustering can consistently identify the clusters of extremes arising in this model. Leveraging this result we propose a simple consistent estimation strategy for learning the angular measure. Our theoretical findings are complemented with numerical experiments illustrating the finite sample performance of our methods.


page 19

page 24

page 25


Kernel PCA for multivariate extremes

We propose kernel PCA as a method for analyzing the dependence structure...

Statistical Inference on a Changing Extremal Dependence Structure

We analyze the extreme value dependence of independent, not necessarily ...

Which Sampling Densities are Suitable for Spectral Clustering on Unbounded Domains?

We consider a random geometric graph with vertices sampled from a probab...

Nonparametric Nearest Neighbor Random Process Clustering

We consider the problem of clustering noisy finite-length observations o...

Concentration bounds for the empirical angular measure with statistical learning applications

The angular measure on the unit sphere characterizes the first-order dep...

Estmiation of the Spectral Measure from Convex Combinations of Regularly Varying Random Vectors

The extremal dependence structure of a regularly varying random vector X...

Estimating an Extreme Bayesian Network via Scalings

Recursive max-linear vectors model causal dependence between its compone...