2-SSVR: A Smooth Support Vector Machine for 2-insensitive Regression

A new smoothing strategy for solving 2-support vector regression (2-SVR), tolerating a small error in fitting a given dataset linearly or nonlinearly, is proposed in this paper. Conventionally, 2-SVR is formulated as a constrained minimization problem, namely a convex quadratic programming problem. We apply the smoothing techniques that have been used for solving the support vector machine for classification, to replace the 2-insensitive loss function by an accurate smooth approximation. This will allow us to solve 2-SVR as an unconstrained minimization problem directly. We term this reformulated problem as 2-smooth support vector regression (2-SSVR). We also prescribe a NewtonArmijo algorithm that has been shown to be convergent globally and quadratically in finite steps to solve our 2-SSVR. In order to handle the case of nonlinear Department of Computer Science & Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 106, [email protected]. Department of Computer Science & Information Engineering, National Chung Cheng University, Chia-Yi, Taiwan 621, [email protected]. ‡ Department of Computer Science & Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 106, [email protected].