Primal twin support vector regression and its sparse approximation

Twin support vector regression (TSVR) obtains faster learning speed by solving a pair of smaller sized support vector machine (SVM)-typed problems than classical support vector regression (SVR). In this paper, a primal version for TSVR, termed primal TSVR (PTSVR), is first presented. By introducing a quadratic function to approximate its loss function, PTSVR directly optimizes the pair of quadratic programming problems (QPPs) of TSVR in the primal space based on a series of sets of linear equations. PTSVR can obviously improve the learning speed of TSVR without loss of the generalization. To improve the prediction speed, a greedy-based sparse TSVR (STSVR) in the primal space is further suggested. STSVR uses a simple back-fitting strategy to iteratively select its basis functions and update the augmented vectors. Computational results on several synthetic as well as benchmark datasets confirm the merits of PTSVR and STSVR. (C) 2010 Elsevier B.V. All rights reserved.