Weighted twin support vector machines with local information and its application.

A Twin Support Vector Machine (TWSVM), as a variant of a Multisurface Proximal Support Vector Machine via Generalized Eigenvalues (GEPSVM), attempts to improve the generalization of GEPSVM, whose solution follows from solving two quadratic programming problems (QPPs), each of which is smaller than in a standard SVM. Unfortunately, the two QPPs still lead to rather high computational costs. Moreover, although TWSVM has better classification performance than GEPSVM, a major disadvantage is it fails to exploit the underlying correlation or similarity information between any pair of data points with the same labels that may be important for classification performance as much as possible. To mitigate the above deficiencies, in this paper, we propose a novel nonparallel plane classifier, called Weighted Twin Support Vector Machines with Local Information (WLTSVM). WLTSVM mines as much underlying similarity information within samples as possible. This method not only retains the superior characteristics of TWSVM, but also has its additional advantages: (1) comparable or better classification accuracy compared to SVM, GEPSVM and TWSVM; (2) taking motivation from standard SVM, the concept of support vectors is retained; (3) more efficient than TWSVM in terms of computational costs; and (4) only one penalty parameter is considered as opposed to two in TWSVM. Finally, experiments on both simulated and real problems confirm the effectiveness of our method.