Abstract
•We propose to use rescaled Hinge loss function for Twin Support Vector Regression with regularizer and name it as Res-TSVR.•We provide the dual formulations of the corresponding optimization problem in Res-TSVR.•We give the analytic convergence proof of Res-TSVR.•Res-TSVR is shown to be robust towards Gaussian and non-Gaussian noise.
In this work, with the help of the rescaled Hinge loss, we propose a twin support vector regression (TSVR) model that is robust to noise. The corresponding optimization problem turns out to be non-convex with smooth l2 regularizer. To solve the problem efficiently, we convert it to its dual form, thereby transforming it into a convex optimization problem. An algorithm, named Res-TSVR, is provided to solve the formulated dual problem. The proof of the convergence of the algorithm is given. It is shown that the maximum number of iterations to achieve an ε-precision solution to the dual problem is O(log(1ε)). We conduct a set of numerical experiments to compare the proposed method with the recently proposed robust approaches of TSVR and the standard SVR. Experimental results reveal that the proposed approach outperforms other robust methods of TSVR in terms of generalization performance and robustness to noise with comparable training time. This claim is based on the experiments performed using seven real-world data sets and three synthetic data sets.