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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/949654 |
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| _version_ | 1849695570316230656 |
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| author | Ling Jian Shuqian Shen Yunquan Song |
| author_facet | Ling Jian Shuqian Shen Yunquan Song |
| author_sort | Ling Jian |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ca421c654f924148bac7e12ba35cd839 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ca421c654f924148bac7e12ba35cd8392025-08-20T03:19:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/949654949654Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace SystemLing Jian0Shuqian Shen1Yunquan Song2College of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaThe 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.http://dx.doi.org/10.1155/2012/949654 |
| spellingShingle | Ling Jian Shuqian Shen Yunquan Song Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System Journal of Applied Mathematics |
| title | Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System |
| title_full | Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System |
| title_fullStr | Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System |
| title_full_unstemmed | Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System |
| title_short | Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System |
| title_sort | improving the solution of least squares support vector machines with application to a blast furnace system |
| url | http://dx.doi.org/10.1155/2012/949654 |
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