Capped Linex Metric Twin Support Vector Machine for Robust Classification

In this paper, a novel robust loss function is designed, namely, capped linear loss function Laε. Simultaneously, we give some ideal and important properties of Laε, such as boundedness, nonconvexity and robustness. Furthermore, a new binary classification learning method is proposed via introducing Laε, which is called the robust twin support vector machine (Linex-TSVM). Linex-TSVM can not only reduce the influence of outliers on Linex-SVM, but also improve the classification performance and robustness of Linex-SVM. Moreover, the effect of outliers on the model can be greatly reduced by introducing two regularization terms to realize the structural risk minimization principle. Finally, a simple and efficient iterative algorithm is designed to solve the non-convex optimization problem Linex-TSVM, and the time complexity of the algorithm is analyzed, which proves that the model satisfies the Bayes rule. Experimental results on multiple datasets demonstrate that the proposed Linex-TSVM can compete with the existing methods in terms of robustness and feasibility.