Adaptive Graph-Based Support Vector Data Description for Weakly-Supervised Anomaly Detection

We propose a novel method for weakly-supervised anomaly detection, where a limited number of labeled normal samples and a sufficient number of unlabeled samples are available for modeling. In particular, we seamlessly integrate label propagation with manifold graph learning into a support vector data description model. Consequently, the estimated manifold graph as well as its parameters will be adaptive to label propagation and benefit the anomaly detection performance. It is superior to most graph-based models that perform manifold graph learning separately by an independent step before label propagation. Theoretically, we derive a stability analysis based on the Rademacher complexity. Further, the effectiveness of the proposed method is demonstrated through several benchmark data sets and a real example of fault detection for high-speed train wheels. Note to Practitioners - This article provides a weakly-supervised anomaly detection method and addresses the challenge of insufficient normal samples for training. The proposed method integrates the adaptive embedded label propagation with adaptive manifold graph learning into a support vector data description model to additionally exploit the intrinsic data distribution information of the unlabeled data in the model formulation. It ensures that the results are jointly optimal for manifold representation and anomaly detection such that the detection accuracy is improved.