The original support vector machine (SVM) uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVM, such as with ${\ell }_1$-regularized. On the other hand, the hinge loss is sensitive to noise. To circumvent these drawbacks, a huberized pinball loss function is proposed. It is less sensitive to noise, similar to the pinball loss which is related to the quantile distance. The proposed loss function is differentiable everywhere and this differentiability can significantly reduce the computational cost for the SVM algorithm. The elastic net penalty is applied to the SVM and the support vector machine classifier with huberized pinball loss (HPSVM) is proposed. Due to the continuous differentiability of the huberized pinball loss function, the Proximal Gradient method is used to solve the proposed model. The numerical experiments on synthetic data, real world datasets confirm the robustness and effectiveness of the proposed method. Statistical comparison is performed to show the significant difference between the proposed method and other compered ones.

原始的支持向量机（SVM）使用铰链损失函数，该函数是不可微的，尤其是对于正则化SVM，例如 ${\ell }_{\mathrm{1个}}$-正规化。另一方面，铰链损耗对噪声敏感。为了克服这些缺点，提出了一种集中化的弹球损失功能。它对噪声不太敏感，类似于与分位数距离相关的弹球损失。所提出的损失函数在任何地方都是可微分的，这种微分可显着降低SVM算法的计算成本。将弹性净罚分法应用于支持向量机，并提出了带有中心化弹球损失的支持向量机分类器（HPSVM）。由于中心化的弹球损失函数具有连续可微性，因此采用近邻梯度法求解该模型。在合成数据和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。