Twin-parametric margin support vector machine with truncated pinball loss

In this paper, we propose a novel classifier termed as twin-parametric margin support vector machine with truncated pinball loss (TPin-TSVM), which is motivated by the twin-parametric margin support vector machine (TPMSVM). The proposed TPin-TSVM has the following characteristics. Firstly, it can preserve both sparsity and feature noise insensitivity simultaneously, because it deals with the quantile distance which makes it less sensitive to noises, and most of the correctly classified samples are given equal penalties which makes it have the precious sparsity. Secondly, it is a non-differentiable non-convex optimization problem, we adopt the popular and effective concave–convex procedure (CCCP) to solve it. In each iteration of CCCP, the TPMSVM is utilized as a core of our TPin-TSVM, because it determines two nonparallel hyperplanes by solving two smaller sized quadratic programming problems, which greatly improves the computational speed. Thirdly, we investigate its theoretical properties of noise insensitivity and sparsity, and the proposed TPin-TSVM realizes the between-class distance maximization, within-class scatter and misclassification error minimization together. The experiments on two artificial datasets also verify the properties. We perform numerical experiments on thirty-five benchmark datasets to investigate the validity of our proposed algorithm. Experimental results indicate that our algorithm yields the comparable generalization performance compared with three state-of-the-art algorithms.