Maximum margin of twin spheres machine with pinball loss for imbalanced data classification

The maximum margin of twin spheres support vector machine (MMTSVM) is an effective method for the imbalanced data classification. However, the hinge loss is used in the MMTSVM and easily leads to sensitivity for the noises and instability for re-sampling. In contrast, the pinball loss is related to the quantile distance and less sensitive to noises. To enhance the performance of MMTSVM, we propose a maximum margin of twin spheres machine with pinball loss (Pin-MMTSM) for the imbalanced data classification in this paper. The Pin-MMTSM finds two homocentric spheres by solving a quadratic programming problem (QPP) and a linear programming problem (LPP). The small sphere captures as many majority samples as possible; and the large sphere pushes out most minority samples by increasing the margin between two homocentric spheres. Moreover, our Pin-MMTSM is equipped with noise insensitivity by employing the pinball loss. Experimental results on eighteen imbalanced datasets indicate that our proposed Pin-MMTSM yields a good generalization performance.