  Extremes play a special role in Anomaly Detection. Beyond inference and
simulation purposes, probabilistic tools borrowed from Extreme Value Theory
(EVT), such as the angular measure, can also be used to design novel
statistical learning methods for Anomaly Detection/ranking. This paper proposes
a new algorithm based on multivariate EVT to learn how to rank observations in
a high dimensional space with respect to their degree of 'abnormality'. The
procedure relies on an original dimension-reduction technique in the extreme
domain that possibly produces a sparse representation of multivariate extremes
and allows to gain insight into the dependence structure thereof, escaping the
curse of dimensionality. The representation output by the unsupervised
methodology we propose here can be combined with any Anomaly Detection
technique tailored to non-extreme data. As it performs linearly with the
dimension and almost linearly in the data (in O(dn log n)), it fits to large
scale problems. The approach in this paper is novel in that EVT has never been
used in its multivariate version in the field of Anomaly Detection.
Illustrative experimental results provide strong empirical evidence of the
relevance of our approach.
