Modified matrix splitting method for the support vector machine and its application to the credit classification of companies in Korea
► We propose a solving approach for the ν-support vector machine (SVM) for classification problems. We use the modified matrix splitting method and incomplete Cholesky decomposition. The matrix splitting method combined with the projection gradient method. The incomplete Cholesky decomposition is us...
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| Published in | Expert systems with applications Vol. 39; no. 10; pp. 8824 - 8834 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.08.2012
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| Abstract | ► We propose a solving approach for the ν-support vector machine (SVM) for classification problems. We use the modified matrix splitting method and incomplete Cholesky decomposition. The matrix splitting method combined with the projection gradient method. The incomplete Cholesky decomposition is used for the large scale Hessian. The proposed method applies for the credit prediction for small-sized Korean companies.
This research proposes a solving approach for the ν-support vector machine (SVM) for classification problems using the modified matrix splitting method and incomplete Cholesky decomposition. With a minor modification, the dual formulation of the ν-SVM classification becomes a singly linearly constrained convex quadratic program with box constraints. The Kernel Hessian matrix of the SVM problem is dense and large. The matrix splitting method combined with the projection gradient method solves the subproblem with a diagonal Hessian matrix iteratively until the solution reaches the optimum. The method can use one of several line search and updating alpha methods in the projection gradient method. The incomplete Cholesky decomposition is used for the calculation of the large scale Hessian and vectors. The newly proposed method applies for a real world classification problem of the credit prediction for small-sized Korean companies. |
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| AbstractList | This research proposes a solving approach for the nu -support vector machine (SVM) for classification problems using the modified matrix splitting method and incomplete Cholesky decomposition. With a minor modification, the dual formulation of the nu -SVM classification becomes a singly linearly constrained convex quadratic program with box constraints. The Kernel Hessian matrix of the SVM problem is dense and large. The matrix splitting method combined with the projection gradient method solves the subproblem with a diagonal Hessian matrix iteratively until the solution reaches the optimum. The method can use one of several line search and updating alpha methods in the projection gradient method. The incomplete Cholesky decomposition is used for the calculation of the large scale Hessian and vectors. The newly proposed method applies for a real world classification problem of the credit prediction for small-sized Korean companies. ► We propose a solving approach for the ν-support vector machine (SVM) for classification problems. We use the modified matrix splitting method and incomplete Cholesky decomposition. The matrix splitting method combined with the projection gradient method. The incomplete Cholesky decomposition is used for the large scale Hessian. The proposed method applies for the credit prediction for small-sized Korean companies. This research proposes a solving approach for the ν-support vector machine (SVM) for classification problems using the modified matrix splitting method and incomplete Cholesky decomposition. With a minor modification, the dual formulation of the ν-SVM classification becomes a singly linearly constrained convex quadratic program with box constraints. The Kernel Hessian matrix of the SVM problem is dense and large. The matrix splitting method combined with the projection gradient method solves the subproblem with a diagonal Hessian matrix iteratively until the solution reaches the optimum. The method can use one of several line search and updating alpha methods in the projection gradient method. The incomplete Cholesky decomposition is used for the calculation of the large scale Hessian and vectors. The newly proposed method applies for a real world classification problem of the credit prediction for small-sized Korean companies. |
| Author | Kim, Jumi Wu, Chih-Hang Lim, Sungmook Kim, Gitae |
| Author_xml | – sequence: 1 givenname: Gitae surname: Kim fullname: Kim, Gitae email: gitaekimemail@gmail.com organization: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2033 Durland Hall, Manhattan, KS 66506, USA – sequence: 2 givenname: Chih-Hang surname: Wu fullname: Wu, Chih-Hang email: chw@ksu.edu organization: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2018 Durland Hall, Manhattan, KS 66506, USA – sequence: 3 givenname: Sungmook surname: Lim fullname: Lim, Sungmook email: sungmook@korea.ac.kr organization: Division of Business Administration, Korea University, Jochiwon-Eup, Yeongi-Gun, Chungnam 339-700, Republic of Korea – sequence: 4 givenname: Jumi surname: Kim fullname: Kim, Jumi email: jmkim@kosbi.re.kr organization: Korea Small Business Institute (KOSBI), 16-2 Yoido-dong, Yeongdeungpo-ku, Seoul 150-742, Republic of Korea |
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| Keywords | Matrix splitting method Support vector machine Company credit prediction Convex programming Incomplete Cholesky decomposition Projection gradient method |
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| Snippet | ► We propose a solving approach for the ν-support vector machine (SVM) for classification problems. We use the modified matrix splitting method and incomplete... This research proposes a solving approach for the nu -support vector machine (SVM) for classification problems using the modified matrix splitting method and... |
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| SubjectTerms | Classification Company credit prediction Convex programming Decomposition Expert systems Incomplete Cholesky decomposition Mathematical analysis Matrix splitting method Projection Projection gradient method Splitting Support vector machine Support vector machines Vectors (mathematics) |
| Title | Modified matrix splitting method for the support vector machine and its application to the credit classification of companies in Korea |
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