Ordinal Regression With Pinball Loss

Ordinal regression (OR) aims to solve multiclass classification problems with ordinal classes. Support vector OR (SVOR) is a typical OR algorithm and has been extensively used in OR problems. In this article, based on the characteristics of OR problems, we propose a novel pinball loss function and present an SVOR method with pinball loss (pin-SVOR). Pin-SVOR is fundamentally different from traditional SVOR with hinge loss. Traditional SVOR employs the hinge loss function, and the classifier is determined by only a few data points near the class boundary, called support vectors, which may lead to a noise sensitive and re-sampling unstable classifier. Distinctively, pin-SVOR employs the pinball loss function. It attaches an extra penalty to correctly classified data that lies inside the class, such that all the training data is involved in deciding the classifier. The data near the middle of each class has a small penalty, and that near the class boundary has a large penalty. Thus, the training data tend to lie near the middle of each class instead of on the class boundary, which leads to scatter minimization in the middle of each class and noise insensitivity. The experimental results show that pin-SVOR has better classification performance than state-of-the-art OR methods.