ν-twin support vector machine with Universum data for classification

Abstract

A novel ?-twin support vector machine with Universum data (U?$\mathfrak {U}_{\nu }$-TSVM) is proposed in this paper. U?$\mathfrak {U}_{\nu }$-TSVM allows to incorporate the prior knowledge embedded in the unlabeled samples into the supervised learning. It aims to utilize these prior knowledge to improve the generalization performance. Different from the conventional U$\mathfrak {U}$-SVM, U?$\mathfrak {U}_{\nu }$-TSVM employs two Hinge loss functions to make the Universum data lie in a nonparallel insensitive loss tube, which makes it exploit these prior knowledge more flexibly. In addition, the newly introduced parameters ?1, ?2 in the U?$\mathfrak {U}_{\nu }$-TSVM have better theoretical interpretation than the penalty factor c in the U$\mathfrak {U}$-TSVM. Numerical experiments on seventeen benchmark datasets, handwritten digit recognition, and gender classification indicate that the Universum indeed contributes to improving the prediction accuracy. Moreover, our U?$\mathfrak {U}_{\nu }$-TSVM is far superior to the other three algorithms (U$\mathfrak {U}$-SVM, ?-TSVM and U$\mathfrak {U}$-TSVM) from the prediction accuracy.