Support Vector Machine Classifier with Pinball Loss

Traditionally, the hinge loss is used to construct support vector machine (SVM) classifiers. The hinge loss is related to the shortest distance between sets and the corresponding classifier is hence sensitive to noise and unstable for re-sampling. In contrast, the pinball loss is related to the quantile distance and the result is less sensitive. The pinball loss has been deeply studied and widely applied in regression but it has not been used for classification. In this paper, we propose a SVM classifier with the pinball loss, called pin-SVM, and investigate its properties, including noise insensitivity, robustness, and misclassification error. Besides, insensitive zone is applied to the pin-SVM for a sparse model. Compared to the SVM with the hinge loss, the proposed pin-SVM has the same computational complexity and enjoys noise insensitivity and re-sampling stability.