论文标题
非线性内核支持向量机，具有0-1软边缘损失
Nonlinear Kernel Support Vector Machine with 0-1 Soft Margin Loss
论文作者
论文摘要
线性支持向量机的最新进展具有0-1软边距损失（$ L_ {0/1} $ - SVM）表明，0-1损耗问题可以直接解决。但是，其理论和算法要求将线性求解框架扩展到其非线性内核形式，因此没有明确表达$ L_ {0/1} $ -SVM的Lagrangian双重功能的明确表达是其中的一个很大的缺陷。在本文中，通过应用非参数表示定理，我们提出了一个非线性模型，用于支撑矢量机，具有0-1软边距损失，称为$ l_ {0/1} $ -KSVM，它谨慎地将核技术涉及其中，更重要的是，成功地解决了它的线性任务。理论上探索了其最佳条件，并引入了乘数（ADMM）算法的交替选择方向方法以获取其数值解决方案。此外，我们首先向$ l_ {0/1} $ -KSVM的支持向量（SV）提出了封闭形式的定义。从理论上讲，我们证明$ L_ {0/1} $ -KSVM的所有SV都位于并行决策表面上。实验部件还表明，$ l_ {0/1} $ - KSVM的SVS较少，同时具有不错的预测准确性，与其线性peer $ L_ {0/1} $ - SVM和其他六个非线性基准标准SVM分类器相比。
Recent advance on linear support vector machine with the 0-1 soft margin loss ($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly. However, its theoretical and algorithmic requirements restrict us extending the linear solving framework to its nonlinear kernel form directly, the absence of explicit expression of Lagrangian dual function of $L_{0/1}$-SVM is one big deficiency among of them. In this paper, by applying the nonparametric representation theorem, we propose a nonlinear model for support vector machine with 0-1 soft margin loss, called $L_{0/1}$-KSVM, which cunningly involves the kernel technique into it and more importantly, follows the success on systematically solving its linear task. Its optimal condition is explored theoretically and a working set selection alternating direction method of multipliers (ADMM) algorithm is introduced to acquire its numerical solution. Moreover, we firstly present a closed-form definition to the support vector (SV) of $L_{0/1}$-KSVM. Theoretically, we prove that all SVs of $L_{0/1}$-KSVM are only located on the parallel decision surfaces. The experiment part also shows that $L_{0/1}$-KSVM has much fewer SVs, simultaneously with a decent predicting accuracy, when comparing to its linear peer $L_{0/1}$-SVM and the other six nonlinear benchmark SVM classifiers.
