Robust transductive support vector machines

In this paper, we propose a robust transductive support vector machine (RTSVM) classifier that is suitable for large-scale data. To this end, we use the robust Ramp loss instead of the Hinge loss for labeled data samples. The resulting optimization problem is non-convex but it can be decomposed to a convex and concave parts. Therefore, the optimization is accomplished iteratively by solving a sequence of convex problems known as concave-convex procedure. Stochastic gradient (SG) is used to solve the convex problem at each iteration, thus the proposed method scales well with large training set size (it is practical for more than a million data) for the linear case.