A multivariate extreme value theory approach to anomaly clustering and visualization

Maël Chiapino, Stephan Clémençon, Vincent Feuillard and Anne Sabourin ()
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Maël Chiapino: LTCI, Télécom Paris, Institut polytechnique de Paris
Stephan Clémençon: LTCI, Télécom Paris, Institut polytechnique de Paris
Vincent Feuillard: Airbus Central R&T, AI Research
Anne Sabourin: LTCI, Télécom Paris, Institut polytechnique de Paris

Computational Statistics, 2020, vol. 35, issue 2, No 9, 607-628

Abstract: 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 $$\mathbf{X }=(X_1,\; \ldots ,\; X_d)$$X=(X1,…,Xd) valued in $$\mathbb {R}^d$$Rd, correspond to the simultaneous occurrence of extreme values for certain subgroups $$\alpha \subset \{1,\; \ldots ,\; d \}$$α⊂{1,…,d} of variables $$X_j$$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 $$\alpha $$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 $$\alpha $$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.

Keywords: Anomaly detection; Clustering; Graph-mining; Latent variable analysis; Mixture modelling; Multivariate extreme value theory; Visualization (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00180-019-00913-y

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