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Anomaly detection is defined as the problem of finding data points that donot follow the patterns of the majority. Among the various proposed methods forsolving this problem, classification-based methods, including one-class SupportVector Machines (SVM) are considered effective and state-of-the-art. Theone-class SVM method aims to find a decision boundary to distinguish betweennormal data points and anomalies using only the normal data. On the other hand,most real-world problems involve some degree of uncertainty, where the trueprobability distribution of each data point is unknown, and estimating it isoften difficult and costly. Assuming partial distribution information such asthe first and second-order moments is known, a distributionally robustchance-constrained model is proposed in which the probability ofmisclassification is low. By utilizing a mapping function to a higherdimensional space, the proposed model will be capable of classifyingorigin-inseparable datasets. Also, by adopting the kernel idea, the need forexplicitly knowing the mapping is eliminated, computations can be performed inthe input space, and computational complexity is reduced. Computational resultsvalidate the robustness of the proposed model under different probabilitydistributions and also the superiority of the proposed model compared to thestandard one-class SVM in terms of various evaluation metrics.

Anomaly Detection Under Uncertainty Using Distributionally Robust Optimization Approach