A Multivariate Extreme Value Theory Approach to Anomaly Clustering and Visualization

Abstract : In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme values for certain subgroups α ⊂ {1,. .. , d} of variables Xj. Under the heavy-tail assumption, which is precisely appropriate for modeling these phenomena, statistical methods relying on multivariate extreme value theory have been developed in the past few years for identifying such events/subgroups. This paper exploits this approach much further by means of a novel mixture model that permits to describe the distribution of extremal observations and where the anomaly type α is viewed as a latent variable. One may then take advantage of the model by assigning to any extreme point a posterior probability for each anomaly type α, defining implicitly a similarity measure between anomalies. It is explained at length how the latter permits to cluster extreme observations and obtain an informative planar representation of anomalies using standard graph-mining tools. The relevance and usefulness of the clustering and 2-d visual display thus designed is illustrated on simulated datasets and on real observations as well, in the aeronautics application domain.
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https://hal.telecom-paristech.fr/hal-02185060
Contributor : Anne Sabourin <>
Submitted on : Tuesday, July 16, 2019 - 1:45:16 PM
Last modification on : Friday, October 18, 2019 - 1:32:36 AM

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  • HAL Id : hal-02185060, version 1
  • ARXIV : 1907.07523

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Maël Chiapino, Stéphan Clémençon, Vincent Feuillard, Anne Sabourin. A Multivariate Extreme Value Theory Approach to Anomaly Clustering and Visualization. 2019. ⟨hal-02185060⟩

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