Fusing Dictionary Learning and Support Vector Machines for Unsupervised Anomaly Detection

We study in this paper the improvement of one-class support vector machines (OC-SVM) through sparse representation techniques for unsupervised anomaly detection. As Dictionary Learning (DL) became recently a common analysis technique that reveals hidden sparse patterns of data, our approach uses this insight to endow unsupervised detection with more control on pattern finding and dimensions. We introduce a new anomaly detection model that unifies the OC-SVM and DL residual functions into a single composite objective, subsequently solved through K-SVD-type iterative algorithms. A closed-form of the alternating K-SVD iteration is explicitly derived for the new composite model and practical implementable schemes are discussed. The standard DL model is adapted for the Dictionary Pair Learning (DPL) context, where the usual sparsity constraints are naturally eliminated. Finally, we extend both objectives to the more general setting that allows the use of kernel functions. The empirical convergence properties of the resulting algorithms are provided and an in-depth analysis of their parametrization is performed while also demonstrating their numerical performance in comparison with existing methods.