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The extreme value support measure machine for group anomaly detection

Lixuan An (UGent) , Bernard De Baets (UGent) and Stijn Luca (UGent)
(2025) MATHEMATICS. 13(11).
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Abstract
Group anomaly detectionis 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, NOVELTY DETECTION, UNINORM

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Citation

Please use this url to cite or link to this publication:

MLA
An, Lixuan, et al. “The Extreme Value Support Measure Machine for Group Anomaly Detection.” MATHEMATICS, vol. 13, no. 11, 2025, doi:10.3390/math13111813.
APA
An, L., De Baets, B., & Luca, S. (2025). The extreme value support measure machine for group anomaly detection. MATHEMATICS, 13(11). https://doi.org/10.3390/math13111813
Chicago author-date
An, Lixuan, Bernard De Baets, and Stijn Luca. 2025. “The Extreme Value Support Measure Machine for Group Anomaly Detection.” MATHEMATICS 13 (11). https://doi.org/10.3390/math13111813.
Chicago author-date (all authors)
An, Lixuan, Bernard De Baets, and Stijn Luca. 2025. “The Extreme Value Support Measure Machine for Group Anomaly Detection.” MATHEMATICS 13 (11). doi:10.3390/math13111813.
Vancouver
1.
An L, De Baets B, Luca S. The extreme value support measure machine for group anomaly detection. MATHEMATICS. 2025;13(11).
IEEE
[1]
L. An, B. De Baets, and S. Luca, “The extreme value support measure machine for group anomaly detection,” MATHEMATICS, vol. 13, no. 11, 2025.
@article{01JWQZ1AHKDTQRPVCYF7695YCS,
  abstract     = {{Group anomaly detectionis 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.}},
  articleno    = {{1813}},
  author       = {{An, Lixuan and De Baets, Bernard and Luca, Stijn}},
  issn         = {{2227-7390}},
  journal      = {{MATHEMATICS}},
  keywords     = {{group anomaly detection,extreme value theory,point processes,one-class support measure machine,uninorm,NOVELTY DETECTION,UNINORM}},
  language     = {{eng}},
  number       = {{11}},
  pages        = {{33}},
  title        = {{The extreme value support measure machine for group anomaly detection}},
  url          = {{http://doi.org/10.3390/math13111813}},
  volume       = {{13}},
  year         = {{2025}},
}
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