The twin support vector machine (TSVM) is widely used in classification problems, but it is not efficient enough for large-scale data sets. Furthermore, to get the optimal parameter, the exhaustive grid search method is applied to TSVM. It is very time-consuming, especially for multiparameter models. Although many techniques have been presented to solve these problems, all of them always affect the performance of TSVM to some extent. In this paper, we propose a safe screening rule (SSR) for linear-TSVM, and give a modified SSR (MSSR) for nonlinear TSVM, which contains multiple parameters. The SSR and MSSR can delete most training samples and reduce the scale of TSVM before solving it. Sequential versions of SSR and MSSR are further introduced to substantially accelerate the whole parameter tuning process. One important advantage of SSR and MSSR is that they are safe, i.e., we can obtain the same solution as the original problem by utilizing them. Experiments on eight real-world data sets and an imbalanced data set with different imbalanced ratios demonstrate the efficiency and safety of SSR and MSSR.

Universum, a third class not belonging to either class of the classification problem, allows to incorporate the prior knowledge into the learning process. A lot of previous work have demonstrated that the Universum is helpful to the supervised and semi-supervised classification. Moreover, Universum has already been introduced into the support vector machine (SVM) and twin support vector machine (TSVM) to enhance the generalisation performance. To further increase the generalisation performance, we propose a least squares TSVM with Universum data ( ${\mathfrak{U}}_{\mathcal{LS}}$-TSVM) in this paper. Our ${\mathfrak{U}}_{\mathcal{LS}}$-TSVM possesses the following advantages: first, it exploits Universum data to improve generalisation performance. Besides, it implements the structural risk minimisation principle by adding a regularisation to the objective function. Finally, it costs less computing time by solving two small-sized systems of linear equations instead of a single larger-sized quadratic programming problem. To verify the validity of our proposed algorithm, we conduct various experiments around the size of labelled samples and the number of Universum data on data-sets including seven benchmark data-sets, Toy data, MNIST and Face images. Empirical experiments indicate that Universum contributes to making prediction accuracy improved even stable. Especially when fewer labelled samples given, ${\mathfrak{U}}_{\mathcal{LS}}$-TSVM is far superior to the improved LS-TSVM (ILS-TSVM), and slightly superior to the $\mathfrak{U}$-TSVM.