R-CTSVM+: Robust capped L1-norm twin support vector machine with privileged information

In the new paradigm, learning using privileged information (LUPI) creates a more informative strategy for tasks to achieve better prediction. SVM based methods including SVM+ and TSVM+, have achieved considerable success in LUPI on the clean data. However, these methods typically suffer from the noise and outliers contained in the data, which leads to larger fluctuations in performance. To handle this problem, in this paper, we propose a novel Robust Capped L1-norm Twin Support Vector Machine with Privileged Information (R-CTSVM+). The proposed pair of regularization functions (up- and down-bound) can definitely help to increase the learning model’s tolerance to disturbance, because the up-bound function aims to maximize the lower bound of the perturbation of both main feature and privilege feature, meanwhile, the down-bound function aims to minimize the upper bound of the perturbation of both main feature and privilege feature. Moreover, as the widely employed squared L2-norm distance typically exaggerates the impact of outliers, we adopt the capped L1 regularized distance to further guarantee the robustness of the model. We present that the resulted optimization problem is theoretically converged and can be solved using an effective alternating optimization procedure. Experimental results on benchmark datasets indicate that the proposed robust model can produce superior performance in the case where data samples contain much noise and outliers.