The previous support vector machine(SVM) including $0/1$ loss SVM, hinge loss
SVM, ramp loss SVM, truncated pinball loss SVM, and others, overlooked the
degree of penalty for the correctly classified samples within the margin. This
oversight affects the generalization ability of the SVM classifier to some
extent. To address this limitation, from the perspective of confidence margin,
we propose a novel Slide loss function ($\ell_s$) to construct the support
vector machine classifier($\ell_s$-SVM). By introducing the concept of proximal
stationary point, and utilizing the property of Lipschitz continuity, we derive
the first-order optimality conditions for $\ell_s$-SVM. Based on this, we
define the $\ell_s$ support vectors and working set of $\ell_s$-SVM. To
efficiently handle $\ell_s$-SVM, we devise a fast alternating direction method
of multipliers with the working set ($\ell_s$-ADMM), and provide the
convergence analysis. The numerical experiments on real world datasets confirm
the robustness and effectiveness of the proposed method.

我们提出了一种基于置信边界的滑动损失函数来构建支持向量机分类器，通过引入近似稳定点的概念和利用利普希茨连续性的性质，我们为滑动支持向量机推导了一阶最优性条件，并定义了滑动支持向量和滑动工作集。为了高效处理滑动支持向量机，我们设计了一种带有滑动工作集的快速交替方向乘子方法，并提供了收敛性分析。在真实世界数据集上的数值实验证实了该方法的鲁棒性和有效性。