关键词: 最小二乘支持向量回归机, 鲁棒, 异常值, 损失函数, 凹凸过程

Abstract: Least Square Support Vector Regression (LS-SVR) is sensitive to noise and outliers. By setting the upper bound of the loss function, a non-convex Ramp loss function was proposed, which had strong ability of suppressing the impact of outliers. Since the Ramp loss function was neither convex nor differentiable and the corresponding non-convex optimization problem was difficult to implement, the Concave-Convex Procedure (CCCP) was employed to transform the non-convex optimization problem into a convex one. Finally, a Newton algorithm was introduced to solve the robust model and the computational complexity was analyzed. The numerical experimental results on artificial and Benchmark data sets show that, in comparison with LS-SVR, the proposed approach has significant robustness to noise and outliers, and it also simultaneously reduces the training time.

Key words: Least Square Support Vector Regression (LS-SVR), robustness, outlier, loss function, Concave-Convex Procedure (CCCP)