Smooth CHKS Twin Support Vector Regression

Twin support vector regression (TSVR) was proposed recently as a novel regressor that tries to find a pair of nonparallel planes, i.e., ε insensitive down- and up- bounds, by solving two related SVM-type problems. However, it may incur suboptimal solution since its objective function is positive semi-definite and it is lack of complexity control. In order to address this shortcoming, smooth twin support vector regression (STSVR) is introduced using sigmoid function as smoothing technique to convert the original problems into unconstrained minimization, which can improve the training speed. However, its accuracy needs to be improved. In this paper, aiming at the low approximation ability of sigmoid function of STSVR, using CHKS (chen-harker-kanzow-smale) function which has better approximation ability as the smooth function, a new version of smooth TSVR called smooth CHKS twin support vector regression (SCTSVR) model is proposed. In SCTSVR, CHKS function is used to approximate the non-differential term of twin support vector regression. Then Newton-Armijo algorithm is used to solve the corresponding model. We have proved that SCTSVR is not only strictly convex, but also can meet the arbitrary order smooth performance. Meanwhile, the experimental results on several artificial and benchmark datasets show that SCTSVR has better regression performance than STSVR.