Robust General Twin Support Vector Machine with Pinball Loss Function

Abstract

AbstractTwin support vector machines (TWSVM) with hinge loss suffer from noise sensitivity and instability. To overcome these issues, pinball loss based general twin support vector machines (Pin-GTSVM) was recently proposed. However, TWSVM and Pin-GTSVM implement the empirical risk minimization principle. Also, the matrices in their dual formulations are positive semi-definite. To overcome these issues, we propose pinball loss based robust general twin support vector machines (Pin-RGTSVM). Pin-RGTSVM implements the structural risk minimization principle which embodies the marrow of statistical learning and pinball loss function makes it more robust for noisy datasets. Also, the matrices appear in the dual formulation of the proposed Pin-RGTSVM are positive definite. The incorporation of the structural risk minimization principle via introduction of the regularisation term leads to the improved generalization performance of the proposed Pin-RGTSVM. Numerical experiments and statistical evaluation on the real world benchmark datasets show the efficacy of the proposed Pin-RGTSVM. KeywordsSupport vector machinesPinball lossTwin support vector machinesHinge loss