Training robust support vector machine with smooth Ramp loss in the primal space

In this paper, we propose a novel robust support vector machine based on the smooth Ramp loss, which has strong ability of suppressing the influences of outliers. The concave–convex procedure (CCCP) is utilized to transform the associated non-convex optimization into a convex one. Then, a Newton-type algorithm is developed to solve the resulting primal optimization of robust support vector machine, and the convergence property and the complexity are discussed. Experimental results show that the proposed approach has significant robustness to outliers and yields better generalization performance than the classical support vector machines on both synthetic and real data sets.