Support vector machine (SVM), as a supervised learning method, has different kinds of varieties with significant performance. In recent years, more research focused on nonparallel SVM, where twin SVM (TWSVM) is the typical one. In order to reduce the influence of outliers, more robust distance measurements are considered in these methods, but the discriminability of the models is neglected. In this article, we propose robust manifold twin bounded SVM (RMTBSVM), which considers both robustness and discriminability. Specifically, a novel norm, that is, capped L1L_{1} -norm, is used as the distance metric for robustness, and a robust manifold regularization is added to further improve the robustness and classification performance. In addition, we also use the kernel method to extend the proposed RMTBSVM for nonlinear classification. We introduce the optimization problems of the proposed model. Subsequently, effective algorithms for both linear and nonlinear cases are proposed and proved to be convergent. Moreover, the experiments are conducted to verify the effectiveness of our model. Compared with other methods under the SVM framework, the proposed RMTBSVM shows better classification accuracy and robustness.

中文翻译：

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具有流形正则化的鲁棒双有界支持向量分类器


支持向量机（SVM）作为一种监督学习方法，种类繁多，性能显着。近年来，更多的研究集中在非并行支持向量机上，其中孪生支持向量机（TWSVM）是典型的。为了减少异常值的影响，这些方法考虑了更鲁棒的距离测量，但忽略了模型的可区分性。在本文中，我们提出了鲁棒流形孪生有界支持向量机（RMTBSVM），它同时考虑了鲁棒性和可辨别性。具体来说，使用一种新颖的范数，即上限L1L_{1}范数作为鲁棒性的距离度量，并添加鲁棒流形正则化以进一步提高鲁棒性和分类性能。此外，我们还使用核方法来扩展所提出的用于非线性分类的RMTBSVM。我们介绍了所提出模型的优化问题。随后，提出了针对线性和非线性情况的有效算法并证明是收敛的。此外，还进行了实验来验证我们模型的有效性。与SVM框架下的其他方法相比，所提出的RMTBSVM表现出更好的分类精度和鲁棒性。