On pairing Huber support vector regression

Abstract In this paper, a novel and efficient pairing support vector regression learning method using e − insensitive Huber loss function (PHSVR) is proposed where the e − insensitive zone having flexible shape is determined by tightly fitting the training samples. Our approach leads to solving a pair of unconstrained minimization problems in primal and the solutions are obtained by two algorithms: a functional iterative (FPHSVR) and Newton iterative (NPHSVR) algorithms. The finite termination of the Newton method to its global minimum solution is proved. The significant advantages of the proposed method are the robustness, generalization ability and learning speed. Experiments performed on a series of synthetic data sets, polluted by different types of noise including heteroscedastic noise and outliers, and on real-world benchmark data sets confirm the effectiveness and superiority of the proposed method.