One-Class Classification Criterion Robust to Anomalies in Training Dataset

A new version of one-class classification criterion robust to anomalies in the training dataset is proposed based on support vector data description (SVDD). The original formulation of the problem is not geometrically correct, since the value of the penalty for the admissible escape of the training sample objects outside the describing hypersphere is incommensurable with the distance to its center in the optimization problem and the presence of outliers can greatly affect the decision boundary. The proposed criterion is intended to eliminate this inconsistency. The equivalent form of criterion without constraints lets us use a kernel-based approach without transition to the dual form to make a flexible description of the training dataset. The substitution of the non-differentiable objective function by the smooth one allows us to apply an algorithm of sequential optimizations to solve the problem. We apply the Jaccard measure for a quantitative assessment of the robustness of a decision rule to the presence of outliers. A comparative experimental study of existing one-class methods shows the superiority of the proposed criterion in anomaly detection.