A safe accelerative approach for pinball support vector machine classifier

Abstract

Support vector machine (SVM) and its extensions have seen many successes in recent years. As an extension to enhance noise insensitivity of SVM, SVM with pinball loss (PinSVM) has attracted much attention. However, existing solvers for PinSVM still have challenges in dealing with large data. In this paper, we propose a safe screening rule for accelerating PinSVM (SSR-PinSVM) to reduce the computational cost. Our proposed rule could identify most inactive instances, and then removes them before solving optimization problem. It is safe in the sense that it guarantees to achieve the exactly same solution as solving original problem. The SSR-PinSVM covers the change of multiple parameters. The existing DVI-SVM can be regarded as a special case of SSR-PinSVM when the parameter τ is constant. Moreover, our screening rule is independent from the solver, thus it can be combined with other fast algorithms. We further provide a dual coordinate descent method for PinSVM (DCDM-PinSVM) as an efficient solver in this paper. Numerical experiments on six artificial data sets, twenty-three benchmark data sets, and a real biological data set have demonstrated the feasibility and validity of our proposed method.