Semi-Supervised Multi-View SVDD via Manifold-Regularized Dictionary Learning for Anomaly Detection

Anomaly detection becomes considerably harder when labels are scarce and the data are described by several heterogeneous views. A handful of labelled samples rarely delineates the normal region well, and the unlabelled pool is itself often contaminated by anomalies, so treating unlabelled data as normal and feeding them into a one-class boundary constraint injects incorrect supervision. We address this with SMDL-SVDD, a semi-supervised multi-view support vector data description (SVDD) framework built on dictionary representation learning. The guiding idea is to let unlabelled samples act at the level of representation rather than the SVDD boundary, so no class assumptions are imposed on them. SMDL-SVDD jointly learns a synthesis and an analysis dictionary in each view to obtain sparse representations, and constrains the SVDD hypersphere using only the small sets of labelled normal and labelled anomalous samples. A graph Laplacian regulariser over all training samples preserves the local manifold structure, while a cross-view consistency term on the unlabelled samples exploits their geometric distribution and shares information across views. The view-specific decision functions are then fused into a single anomaly score. We solve the joint problem by alternating convex search and analyse its convergence. Across 23 anomaly detection tasks derived from six public datasets, SMDL-SVDD gives the highest area under the receiver operating characteristic curve (AUC) on 21, improving the mean AUC by 8.87-10.62 percentage points over single-view one-class methods, by 5.10-7.64 points over representative semi-supervised detectors and by 4.11-5.24 points over multi-view one-class methods. Significance, noise, label-ratio, parameter, convergence, ablation and runtime studies confirm that the gains are stable; the ablation shows that manifold regularisation contributes substantially to the improvement and acts complementarily to the cross-view consistency constraint.