Robust one-class kernel spectral regression

The kernel null-space technique is known to be an effective one-class classification (OCC) technique. Nevertheless, the applicability of this method is limited due to its susceptibility to possible training data corruption and the inability to rank training observations according to their conformity with the model. This article addresses these shortcomings by regularizing the solution of the null-space kernel Fisher methodology in the context of its regression-based formulation. In this respect, first, the effect of the Tikhonov regularization in the Hilbert space is analyzed, where the one-class learning problem in the presence of contamination in the training set is posed as a sensitivity analysis problem. Next, the effect of the sparsity of the solution is studied. For both alternative regularization schemes, iterative algorithms are proposed which recursively update label confidences. Through extensive experiments, the proposed methodology is found to enhance robustness against contamination in the training set compared with the baseline kernel null-space method, as well as other existing approaches in the OCC paradigm, while providing the functionality to rank training samples effectively.