A Weighted Least Squares Twin Support Vector Machine

Least squares twin support vector machine (LS-TSVM) aims at resolving a pair of smaller-sized quadratic programming problems (QPPs) instead of a single large one as in the conventional least squares support vector machine (LS-SVM), which makes the learning speed of LS-TSVM faster than that of LS-SVM. However, same penalties are given to the negative samples when constructing the hyper-plane for the positive samples. Moreover the use of square of 2-norm of slack variables neglects the effects of samples in different positions, which easily results in poor performance. In fact, the negative samples staying at different positions have different effects on the separating hyper-plane. To overcome these disadvantages and enhance the generalization performance of classifier, we propose a weighted LS-TSVM in this paper. Different penalties are given to the samples depending on their different positions in our weighted LS-TSVM. Finally our proposed algorithm yields greater generalization performance in comparison with three other algorithms. Numerical experiments on eight benchmark datasets demonstrate the feasibility and validity of our proposed algorithm.