Some New Support Vector Machine Models under Given Empirical Risk

The problem of designing a SVM with given empirical risk as well as good generalization ability is proposed in this paper. Some new SVM models, by minimizing the confident risk under given empirical risk, are proposed to achieve this aim. The solving methods for these models are also discussed. It is shown that the smoothing technique is more suitable to solve these models. A numerical experiment is carried out to claim that the empirical risks of these models are well controlled. The main advantage of these models is of good interactive. The trade-off between the empirical risk and the confident risk can be controlled more easily than traditional SVM models. These models are especially adaptive to the problems, in which the distributions of two types of sample are unbalance or the costs of two types of errors are unequal.