A weighted twin support vector regression

Twin support vector regression (TSVR) is a new regression algorithm, which aims at finding epsilon-insensitive up- and down-bound functions for the training points. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one in a classical SVR. However, the same penalties are given to the samples in TSVR. In fact, samples in the different positions have different effects on the bound function. Then, we propose a weighted TSVR in this paper, where samples in the different positions are proposed to give different penalties. The final regressor can avoid the over-fitting problem to a certain extent and yield great generalization ability. Numerical experiments on one artificial dataset and nine benchmark datasets demonstrate the feasibility and validity of our proposed algorithm. (C) 2012 Elsevier B.V. All rights reserved.