Research On Robust Support Vector Machines

Support vector machine(SVM) is a machine learning method based on statistical learning theory. For its good generalization ability, SVM has achieved extensive attention. In real-world applications, SVM demonstrates better performance in comparison with the other traditional learning methods. The classification problems of SVM involve not only two-class classification and multi-class classification, but also one-class classification in real application. However, two-class classification and one-class classification both need to solve convex quadratic programming problem with linear constrains. Then, the optimization technique of standard quadratic form is utilized to solve the dual optimization problem of the foresaid quadratic programming. The L2 norm based generalization term in the quadratic programming is strongly sensitive to noise. At the same time, since classification hyper-plane relies only on small part of training samples, it becomes very sensitive to noise.To enhance the anti-noise ability and generalization performance of SVM for tackling two-class and one-class classification problems, robust smooth SVM and robust one-class smooth SVM are proposed, respectively. The main contributions of the thesis contain:① The smooth technique is utilized to reformulate the quadratic programming problem of the traditional SVM as an unconstrained optimization problem. Thus, the strong convexity and differentiability of SVM are enhanced.② M-estimator is used to substitute the L2 norm based regularization term of SVM. Therefore, the sensitivity of L2 norm to noise can be avoided and the anti-noise ability can be enhanced.③ The half-quadratic minimization method is used to solve the optimization problems of the proposed models. When the size of data set becomes larger, the running efficiency of the half-quadratic minimization method is relatively high.Experimental results demonstrate that the proposed method can efficiently enhance the robustness of SVM for tackling two-class classification and one-class classification.