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Journal of Applied MathematicsVolume 2012 2012, Article ID 949654, 12 pages

Research ArticleCollege of Science, China University of Petroleum, Qingdao 266580, China

Received 4 May 2012; Revised 23 August 2012; Accepted 20 September 2012

Academic Editor: Chuanhou Gao

Copyright © 2012 Ling Jian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The solution of least squares support vector machines LS-SVMs is characterized by a specific linearsystem, that is, a saddle point system. Approaches for its numerical solutions such as conjugatemethods Sykens and Vandewalle 1999 and null space methods Chu et al. 2005 have been proposed. To speed up the solution of LS-SVM, thispaper employs the minimal residual MINRES method to solve the above saddle point system directly. Theoretical analysis indicates that the MINRES method is more efficient than the conjugate gradientmethod and the null space method for solving the saddle point system. Experiments on benchmark datasets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantlyreduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRESmethod is used to track a practical problem originated from blast furnace iron-making process: changingtrend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectivelyperform feature reduction and model selection simultaneously, so it is a practical tool for the silicontrend prediction task.

Author: Ling Jian, Shuqian Shen, and Yunquan Song



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