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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-paris.fr/hal-02461861
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Submitted on : Thursday, January 30, 2020 - 11:41:34 PM
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Mael Chiapino, Stéphan Clémençon, Vincent Feuillard, Anne Sabourin. A multivariate extreme value theory approach to anomaly clustering and visualization. Computational Statistics, Springer Verlag, 2019, ⟨10.1007/s00180-019-00913-y⟩. ⟨hal-02461861⟩

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