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Journal of Applied Mathematics
Volume 2012, Article ID 949654, 12 pages
Research Article

Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System

College 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 linear system, that is, a saddle point system. Approaches for its numerical solutions such as conjugate methods Sykens and Vandewalle (1999) and null space methods Chu et al. (2005) have been proposed. To speed up the solution of LS-SVM, this paper 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 gradient method and the null space method for solving the saddle point system. Experiments on benchmark data sets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantly reduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRES method is used to track a practical problem originated from blast furnace iron-making process: changing trend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectively perform feature reduction and model selection simultaneously, so it is a practical tool for the silicon trend prediction task.