Smooth Twin Bounded Support Vector Machine with Pinball Loss

Abstract

The twin support vector machine improves the classification performance of the support vector machine by solving two smaller quadratic programming problems. However, for the twin support vector machine and some of its variants, the constructed models are usually transformed from the original space into the dual space to obtain the solutions. Meanwhile, the hinge loss function used in above models is sensitive to noise and unstable in resampling. In order to further improve the performance of the twin support vector machine, the pinball loss function is introduced into the twin bounded support vector machine directly, and the non-differentiable problem of the pinball loss function at zero is solved by constructing a smooth approximation function. Based on this, a smooth twin bounded support vector machine model with pinball loss is obtained. The model is solved iteratively in the original space by using the Newton-Armijo method, then a smooth twin bounded support vector machine with pinball loss algorithm is proposed. In the experiments, the proposed twin support vector machine is validated on the UCI datasets, which shows the effectiveness of the proposed algorithm.