LAUSR

The projection twin support vector machine (PTSVM) is a potential tool for classification problem. However the loss function of PTSVM is hinge loss function which is a unbounded loss and not robust enough to outliers. In this work, a robust PTSVM (termed RSHPTSVM) is proposed based on rescaled square hinge loss (RSH-loss) to handle classification problem. A close relationship between RSH-loss and correntropy is established theoretically. The RSH-loss can be viewed as a correntropy-induced loss by a reproducing piecewise kernel. As such a correntropy loss, it has vastly different properties from hinge loss such as boundedness, robustness and nonconvexity. Moreover, RSH-loss is with higher order statistical information from samples. However the nonconvexity of RSHPTSVM makes it difficult to optimize, so that an efficient iterative optimization algorithm based on semi-quadratic optimization theory is proposed to solve RSHPTSVM, which can quickly converge to the optimal solution. Furthermore, we extend our RSHPTSVM from binary classification to multi-classification and propose a robust projection multi-birth support vector machine model (termed RSHPMBSVM). The proposed method is implemented on various datasets including three artificial datasets, UCI datasets, and a practical application dataset. The experiment results under no noise and label noise circumstance confirm the feasibility and effectiveness of the proposed methods.