This paper proposes a new robust truncated L\(_2\)-norm twin support vector machine (T\(^2\)SVM), where the truncated L\(_2\)-norm is used to measure the empirical risk to make the classifiers more robust when encountering lots of outliers. Meanwhile, chance constraints are also employed to specify false positive and false negative error rates. T\(^2\)SVM considers a pair of chance constrained nonconvex nonsmooth problems. To solve these difficult problems, we propose an efficient iterative method for T\(^2\)SVM based on difference of convex functions (DC) programs and DC Algorithms (DCA). Experiments on benchmark data sets and artificial data sets demonstrate the significant virtues of T\(^2\)SVM in terms of robustness and generalization performance.

本文提出了一种新的鲁棒截断L \(_2\) -范数孪生支持向量机(T \(^2\) SVM)，其中截断的L \(_2\) -范数用于衡量经验风险，使当遇到大量异常值时，分类器更加稳健。同时，还使用机会约束来指定假阳性和假阴性错误率。T \(^2\) SVM 考虑一对机会约束的非凸非光滑问题。为了解决这些难题，我们提出了一种基于凸函数 (DC) 程序和 DC 算法 (DCA) 差异的T \(^2\) SVM的高效迭代方法。在基准数据集和人工数据集上的实验证明了 T \(^2\)的显着优点SVM 在鲁棒性和泛化性能方面。