A maximum margin and minimum volume hyper-spheres machine with pinball loss for imbalanced data classification

The twin hyper-sphere support vector machine (THSVM) classifies two classes of samples via two hyper-spheres instead of a pair of nonparallel hyper-planes as in the conversional twin support vector machine (TSVM). Moreover THSVM avoids the matrix inverse operation when solving two dual quadratic programming problems (QPPs). However it cannot yield a desirable result when dealing with the imbalanced data classification. To improve the generalization performance, we propose a maximum margin and minimum volume hyper-spheres machine with pinball loss (Pin-M3HM) for the imbalanced data classification in this paper. The basic idea is to construct two hyper-spheres with different centers and radiuses in a sequential order. The first one contains as many examples in majority class as possible, and the second one covers minority class of examples as possible. Moreover the margin between two hyper-spheres is as large as possible. Besides, the pinball loss function is introduced into it to avoid the noise disturbance. Experimental results on 24 imbalanced datasets from the repositories of UCI and KEEL, and a real spectral dataset of Chinese grape wines indicate that our proposed Pin-M3HM yields a good generalization performance for the imbalanced data classification.