Joint rescaled asymmetric least squared nonparallel support vector machine with a stochastic quasi-Newton based algorithm

A host of literatures have shown that the standard support vector machine (SVM), induced by the hinge loss function, is unstable for re-sampling (feature noise) and sensitive to outliers (label noise). In this paper, we propose a novel rescaled asymmetric least squared geometric twin parametric-margin SVM (RaLS-GTPSVM) for binary classification issues with feature noise and label noise. The constructed method is consistent and can obtain two nonparallel boundary hyperplanes using one SVM-type optimization problem. We theoretically discuss several properties of the RaLS-GTPSVM, such as the outlier insensitivity and the Fisher consistency. A stochastic quasi-Newton (SQN) -based half-quadratic (HQ) algorithm is implemented for solving the RaLS-GTPSVM. The convergence of the SQN-based HQ procedure is proved. To demonstrate the superiority of the proposed RaLS-GTPSVM, we conduct extensive numerical studies on both synthetic and real datasets, in comparison with several existing famous methods.