Partially Supervised Anomaly Detection Using Convex Hulls on a 2D Parameter Space

Anomaly detection is the problem of identifying objects appearing to be inconstistent with the remainder of that set of data. Detecting such samples is useful on various applications such as fault detection, fraud detection and diagnostic systems. Partially supervised methods for anomaly detection are interesting because they only need data labeled as one of the classes (normal or abnormal). In this paper, we propose a partially supervised framework for anomaly detection based on convex hulls in a parameter space, assuming a given probability distribution. It can be considered a framework since it support any distribution or combination of distribution, modelling only normal samples. We investigated an algorithm based on this framework, assuming the normal distribution for the not anomalous data and compared the results with statistical algorithms, the One-class SVM and Naive Bayes classifiers. The proposed method performed well and showed results comparable or better than the competing methods. Furthermore, this approach can handle any probability distribution or mixture of distributions, allowing the user to choose a parameter space that better models the problem of finding anomalies.