{"ID":3083859,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T05:49:02.101151534Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05814","arxiv_id":"2606.05814","title":"Robust and sparse support vector machine via hybrid truncated loss for supervised classification","abstract":"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 ($L_{\\mathrm{ht}}$) that is both sparse and bounded, and build the $L_{\\mathrm{ht}}$-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 $L_{\\mathrm{ht}}$-SVM to multi-view learning by adding structural information and view weights, resulting in Mv$L_{\\mathrm{ht}}$-SVM, which follows both the consensus and complementarity principles. Experiments on synthetic, real-world, and image datasets show that $L_{\\mathrm{ht}}$-SVM achieves higher accuracy with fewer support vectors and better noise robustness than five single-view methods, while Mv$L_{\\mathrm{ht}}$-SVM outperforms six multi-view methods in accuracy, precision, recall, and F1-score.","short_abstract":"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 tr...","url_abs":"https://arxiv.org/abs/2606.05814","url_pdf":"https://arxiv.org/pdf/2606.05814v1","authors":"[\"Yuliang Yang\",\"Chen Chen\",\"Yuxiang Liu\",\"Huiru Wang\"]","published":"2026-06-04T07:53:48Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}