Anomaly Detection Under Uncertainty Using Distributionally Robust Optimization Approach

Abstract

Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various proposed methods for solving this problem, classification-based methods, including one-class Support Vector Machines (SVM) are considered effective and state-of-the-art. The one-class SVM method aims to find a decision boundary to distinguish between normal data points and anomalies using only the normal data. On the other hand, most real-world problems involve some degree of uncertainty, where the true probability distribution of each data point is unknown, and estimating it is often difficult and costly. Assuming partial distribution information such as the first and second-order moments is known, a distributionally robust chance-constrained model is proposed in which the probability of misclassification is low. By utilizing a mapping function to a higher dimensional space, the proposed model will be capable of classifying origin-inseparable datasets. Also, by adopting the kernel idea, the need for explicitly knowing the mapping is eliminated, computations can be performed in the input space, and computational complexity is reduced. Computational results validate the robustness of the proposed model under different probability distributions and also the superiority of the proposed model compared to the standard one-class SVM in terms of various evaluation metrics.