Robust and sparse support vector machine via hybrid truncated loss for supervised classification

The support vector machine (SVM) is a widely used classifier, but choosing an appropriate loss function remains difficult. Convex losses such as the hinge loss and least-squares loss are sensitive to outliers, while bounded non-convex losses often lead to high computational cost. To address this, we propose a hybrid truncated loss function (Lht) that is both sparse and bounded, and build the Lht-SVM model for single-view classification. We introduce the P-stationary point and use it to establish the first-order necessary and sufficient optimality conditions. Based on these conditions, we design an alternating direction method of multipliers with a working-set strategy that reduces computational cost and achieves global convergence. We further extend Lht-SVM to multi-view learning by adding structural information and view weights, resulting in MvLht-SVM, which follows both the consensus and complementarity principles. Experiments on synthetic, real-world, and image datasets show that Lht-SVM achieves higher accuracy with fewer support vectors and better noise robustness than five single-view methods, while MvLht-SVM outperforms six multi-view methods in accuracy, precision, recall, and F1-score.