The Extreme Value Support Measure Machine for Group Anomaly Detection

Lixuan An (), Bernard De Baets and Stijn Luca
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Lixuan An: Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium
Bernard De Baets: Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium
Stijn Luca: Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium

Mathematics, 2025, vol. 13, issue 11, 1-33

Abstract: Group anomaly detection is a subfield of pattern recognition that aims at detecting anomalous groups rather than individual anomalous points. However, existing approaches mainly target the unusual aggregate of points in high-density regions. In this way, unusual group behavior with a number of points located in low-density regions is not fully detected. In this paper, we propose a systematic approach based on extreme value theory (EVT), a field of statistics adept at modeling the tails of a distribution where data are sparse, and one-class support measure machines (OCSMMs) to quantify anomalous group behavior comprehensively. First, by applying EVT to a point process model , we construct an analytical model describing the likelihood of an aggregate within a group with respect to low-density regions, aimed at capturing anomalous group behavior in such regions. This model is then combined with a calibrated OCSMM, which provides probabilistic outputs to characterize anomalous group behavior in high-density regions, enabling improved assessment of overall anomalous group behavior. Extensive experiments on simulated and real-world data demonstrate that our method outperforms existing group anomaly detectors across diverse scenarios, showing its effectiveness in quantifying and interpreting various types of anomalous group behavior.

Keywords: group anomaly detection; extreme value theory; point processes; one-class support measure machine; uninorm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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