Weighted twin support vector machine with rescaled hinge loss

Abstract Weighted twin support vector machine (WTSVM) has been proved to be effective for classification problems. However, it is sensitive to noises, especially for data corrupted by outliers. In this paper, we propose an improved classifier termed as weighted twin support vector machine with rescaled hinge loss (RHWTSVM). Similar to WTSVM, it uses the intra-class KNN technique to extract structural information in the same class. It uses the inter-class KNN technique to reduce the redundant constraints to improve the computational speed. Furthermore, we introduce the regularization term into the objective function to make the proposed RHWTSVM implement the principles of structural risk minimization and empirical risk minimization simultaneously. Besides, we use the rescaled hinge loss function which is a monotonic, bounded, and nonconvex loss to replace the traditional hinge loss function in WTSVM to make the proposed classifier more robust. Therefore, the RHWTSVM is less sensitive to outliers. Because the model is a nonconvex optimization problem, we use the half-quadratic optimization method to solve it and find that the new method is equivalent to an iterative WTSVM. Numerical experiments on datasets with various levels of noise demonstrate that RHWTSVM is reasonable and effective.