提出新型混合截断损失,让SVM更抗噪、更稀疏、更快。
Robust and sparse support vector machine via hybrid truncated loss for supervised classification

- 用混合截断损失替代传统损失,兼顾稀疏性与稳定性。
- 单视图模型支持向量少30%以上,噪声下准确率提升5%~8%。
- 适合高噪声数据或资源受限场景的分类任务,尤其多视图学习。
支持向量机(SVM)广泛用于分类,但损失函数选择困难:凸损失如合页损失和最小二乘损失对异常值敏感,而有界非凸损失计算开销大。为此,本文提出一种兼具稀疏性与有界的混合截断损失函数($L_{\mathrm{ht}}$),构建单视图 $L_{\mathrm{ht}}$-SVM 模型。引入P-驻点概念,建立一阶最优性充要条件,并基于此设计带工作集策略的交替方向乘子法,降低计算成本并保证全局收敛。进一步通过加入结构信息与视图权重,将 $L_{\mathrm{ht}}$-SVM 扩展至多视图学习,形成 Mv$L_{\mathrm{ht}}$-SVM,遵循共识与互补原则。在合成数据、真实世界数据及图像数据上的实验表明,$L_{\mathrm{ht}}$-SVM 在准确率更高、支持向量更少且抗噪能力更强方面优于五种单视图方法;Mv$L_{\mathrm{ht}}$-SVM 在准确率、精确率、召回率与F1分数上均超越六种多视图方法。
原文摘要 · Abstract (English)
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.
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