2019
DOI: 10.1007/s00180-019-00913-y
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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 ide… Show more

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Cited by 9 publications
(5 citation statements)
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“…Hence, the findings are focused on these two extreme clusters. Chiapino et al (2020) also suggest focusing on extreme values (extreme value theory [EVT]) to analyze patterns and structure in data. Similarly, EVT is extensively used in risk management research to identify data clusters that are associated with high or low values (Embrechts et al , 1999), in our case the most resilient and the most vulnerable other clusters (please see Figure 1).…”
Section: Resultsmentioning
confidence: 99%
“…Hence, the findings are focused on these two extreme clusters. Chiapino et al (2020) also suggest focusing on extreme values (extreme value theory [EVT]) to analyze patterns and structure in data. Similarly, EVT is extensively used in risk management research to identify data clusters that are associated with high or low values (Embrechts et al , 1999), in our case the most resilient and the most vulnerable other clusters (please see Figure 1).…”
Section: Resultsmentioning
confidence: 99%
“…analyzing the extremes of a high dimensional random vector. Such studies can be divided into the following categories: clustering methods [6,7,39], support identification, [32,33,8,9,53,44], Principal Component Analysis of the angular component of extremes [14,41,20], and graphical models for extremes [36,23,1]; see also [24] and the references therein. Our approach is remotely related to the last category: extremal graphical models.…”
Section: Dimensionality Reduction In Evtmentioning
confidence: 99%
“…How to use EVT in a machine learning framework has received increasing attention in the past few years. Learning tasks considered so far include anomaly detection Roberts (1999Roberts ( , 2000; Clifton et al (2011); Goix et al (2016); Thomas et al (2017), anomaly clustering Chiapino et al (2019a), unsupervised learning Goix et al (2015), online learning Carpentier & Valko (2014); Achab et al (2017), dimension reduction and support identification Goix et al (2017); Chiapino & Sabourin (2016); Chiapino et al (2019b). The present paper builds upon the methodological framework proposed by Jalalzai et al (2018) for classification in extreme regions.…”
Section: Introductionmentioning
confidence: 97%