Convex and nonconvex nonparametric frontier-based classification methods for anomaly detection
Résumé
Efective 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 frontierbased classifcation (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 refecting 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 outputlike characteristic variables are incorporated. In addition, by allowing some of
the training observations to be misclassifed, 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 classifcation performance and have
consistent advantages in detecting abnormal samples, especially the nonconvexNPFC methods.