<p>Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various methods proposed for solving this problem, classification-based methods, including one-class support vector machine (SVM), are considered effective and promising. Most real-world problems involve some degree of uncertainty, where not only are the data points uncertain, but also their true probability distributions are unknown. In this paper, considering some given partial distribution information such as the first- and second-order moments, a novel distributionally robust chance-constrained model is proposed. This model provides low misclassification error and can classify origin-inseparable data by utilizing a mapping function to a higher-dimensional space. Moreover, by adopting the kernel idea, the need for explicitly knowing the mapping function is eliminated, and computational complexity is reduced. Computational results validate the robustness of the proposed model against uncertainty in the feature vectors of data points and their probability distributions. The superiority of the proposed model compared to some benchmark models in terms of various evaluation metrics is evident.</p>

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Distributionally robust one-class support vector machine for anomaly detection under uncertainty

  • Amirhossein Noormohammadi,
  • Seyed Ali MirHassani,
  • Farnaz Hooshmand Khaligh

摘要

Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various methods proposed for solving this problem, classification-based methods, including one-class support vector machine (SVM), are considered effective and promising. Most real-world problems involve some degree of uncertainty, where not only are the data points uncertain, but also their true probability distributions are unknown. In this paper, considering some given partial distribution information such as the first- and second-order moments, a novel distributionally robust chance-constrained model is proposed. This model provides low misclassification error and can classify origin-inseparable data by utilizing a mapping function to a higher-dimensional space. Moreover, by adopting the kernel idea, the need for explicitly knowing the mapping function is eliminated, and computational complexity is reduced. Computational results validate the robustness of the proposed model against uncertainty in the feature vectors of data points and their probability distributions. The superiority of the proposed model compared to some benchmark models in terms of various evaluation metrics is evident.