Sparse pinball Universum nonparallel support vector machine and its safe screening rule

Abstract

Nonparallel support vector machine (NPSVM) is an effective and popular classification technique, which introduces the \(\epsilon \)-insensitive loss function instead of the quadratic loss function in twin support vector machine (TSVM), making the model have the same sparsity and kernel strategy as support vector machine (SVM). However, NPSVM is sensitive to noise points and does not utilize the prior knowledge embedded in the unlabeled samples. Therefore, to improve its generalization ability and robustness, a sparse pinball Universum nonparallel support vector machine (SPUNPSVM) is first proposed in this paper. On the one hand, the sparse pinball loss is employed to enhance the robustness. On the other hand, it exploits the Universum data, which do not belong to any class, to embed prior knowledge into the model. Numerical experiments have verified its effectiveness. Furthermore, to further speed up SPUNPSVM, we propose a safe screening rule (SSR-SPUNPSVM) based on its sparsity, which achieves acceleration without sacrificing accuracy. Numerical experiments and statistical tests demonstrate the superiority of our SSR-SPUNPSVM.