Primal twin support vector regression and its sparse approximation

  • Authors:
  • Xinjun Peng

  • Affiliations:
  • Department of Mathematics, Shanghai Normal University, 200234, PR China and Scientific Computing Key Laboratory of Shanghai Universities, 200234, PR China

  • Venue:
  • Neurocomputing
  • Year:
  • 2010

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Abstract

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.