KNN-based weighted rough ν-twin support vector machine.

Twin support vector classification (TSVM) finds two nonparallel hyper-planes by solving a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one as in the classical support vector machine (SVM), which makes the learning speed of TSVM approximately four times faster than that of the standard SVM. However the same penalties are given to the samples, which reduces the classification accuracy of TSVM. To improve the classification accuracy, rough ν-TSVM was proposed, where different penalties are given to the negative samples depending on their different positions when constructing separating hyper-plane for the positive samples. But the local information of positive samples is not exploited, and each positive sample shares the same weights in it. In fact, they have different effects on the separating hyper-planes. Inspired by the studies above, we propose a K-nearest neighbor (KNN)-based weighted rough ν-twin support vector machine (Weighted rough ν-TSVM) in this paper, in which not only different penalties are given to one class of samples, but also different weights are given to the other class of samples. So weighted rough ν-TSVM yields higher testing accuracy in comparison with the state-of-the-art algorithms. Moreover, weighted rough ν-TSVM costs lower than other algorithms since some redundant constraints are deleted. In addition, the influence of different number K of clusters is also discussed in this paper. Numerical experiments on forty-two benchmark datasets are performed to investigate the validity of our proposed algorithm. Experimental results show the effectiveness of our proposed algorithm.