Smooth 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., epsilon-insensitive up- and down-bounds, by solving two related SVM-type problems. However, it may incur suboptimal solution since its objective function is positive semi-definite and the lack of complexity control. In order to address this shortcoming, we develop a novel SVR algorithm termed as smooth twin SVR (STSVR). The idea is to reformulate TSVR as a strongly convex problem, which results in unique global optimal solution for each subproblem. To solve the proposed optimization problem, we first adopt a smoothing technique to convert the original constrained quadratic programming problems into unconstrained minimization problems, and then use the well-known Newton-Armijo algorithm to solve the smooth TSVR. The effectiveness of the proposed method is demonstrated via experiments on synthetic and real-world benchmark datasets.