A weighted twin support vector regression

Twin support vector regression (TSVR) is a new regression algorithm, which aims at finding ϵ-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.