All-in-one multicategory Ramp loss maximum margin of twin spheres support vector machine

Maximum margin of twin spheres support vector machine (MMTSSVM) is effective to deal with imbalanced data classification problems. However, it is sensitive to outliers because of the use of the Hinge loss function. To enhance the stability of MMTSSVM, we propose a Ramp loss maximum margin of twin spheres support vector machine (Ramp-MMTSSVM) in this paper. In terms of the Ramp loss function, the outliers can be given fixed loss values, which reduces the negative effect of outliers on constructing models. Since Ramp-MMTSSVM is a non-differentiable non-convex optimization problem, we adopt Concave-Convex Procedure (CCCP) approach to solve it. We also analyze the properties of parameters and verify them by one artificial experiment. Besides, we use Rest-vs.-One(RVO) strategy to extend Ramp-MMTSSVM to multi-class classification problems. The experimental results on twenty benchmark datasets indicate that no matter in binary or multi-class classification cases, our approaches both can obtain better experimental performance than the compared algorithms.