Convex and nonconvex nonparametric frontier-based classification methods for anomaly detection

Qianying Jin (), Kristiaan Kerstens and Ignace Van de Woestyne ()
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Qianying Jin: Nanjing University of Aeronautics and Astronautics
Ignace Van de Woestyne: Brussels Campus

OR Spectrum: Quantitative Approaches in Management, 2024, vol. 46, issue 4, No 6, 1213-1239

Abstract: Abstract Effective methods for determining the boundary of the normal class are very useful for detecting anomalies in commercial or security applications—a problem known as anomaly detection. This contribution proposes a nonparametric frontier-based classification (NPFC) method for anomaly detection. By relaxing the commonly used convexity assumption in the literature, a nonconvex-NPFC method is constructed and the nonconvex nonparametric frontier turns out to provide a more conservative boundary enveloping the normal class. By reflecting on the monotonic relation between the characteristic variables and the membership, the proposed NPFC method is in a more general form since both input-like and output-like characteristic variables are incorporated. In addition, by allowing some of the training observations to be misclassified, the convex- and nonconvex-NPFC methods are extended from a hard nonparametric frontier to a soft one, which also provides a more conservative boundary enclosing the normal class. Both simulation studies and a real-life data set are used to evaluate and compare the proposed NPFC methods to some well-established methods in the literature. The results show that the proposed NPFC methods have competitive classification performance and have consistent advantages in detecting abnormal samples, especially the nonconvex-NPFC methods.

Keywords: Nonparametric frontier; Convex; Nonconvex; Anomaly detection (search for similar items in EconPapers)
Date: 2024
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Working Paper: Convex and nonconvex nonparametric frontier-based classification methods for anomaly detection (2024)
Working Paper: Convex and Nonconvex Nonparametric Frontier-based Classification Methods for Anomaly Detection (2023)
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DOI: 10.1007/s00291-024-00751-5

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