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

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.