An improved ν-twin support vector machine

Twin support vector machine (TSVM) is regarded as a milestone in the development of the powerful SVM. It finds two nonparallel planes by resolving a pair of smaller-sized quadratic programming problems rather than a single large one, which makes the learning speed of TSVM approximately four times faster than that of the standard SVM. However, the empirical risk minimization principle is implemented in the TSVM, so it easily leads to the over-fitting problem and reduces the prediction accuracy of the classifier. nu-TSVM, as a variant of TSVM, also implements the empirical risk minimization principle. To enhance the generalization ability of the classifier, we propose an improved nu-TSVM by introducing a regularization term into the objective function, so there are two parts in the objective function, one of which is to maximize the margin between the two parallel hyper-planes, and the other one is to minimize the training errors of two classes of samples. Therefore the structural risk minimization principle is implemented in our improved nu-TSVM. Numerical experiments on one artificial dataset and nine benchmark datasets show that our improved nu-TSVM yields better generalization performance than SVM, nu-SVM, and nu-TSVM. Moreover, numerical experiments with different proportions of outliers demonstrate that our improved nu-TSVM is robust and stable. Finally, we apply our improved nu-TSVM to two BCI competition datasets, and also obtain better prediction accuracy.