Modified matrix splitting method for the support vector machine and its application to the credit classification of companies in Korea - Kim, Gitae; Wu, Chih-Hang; Lim, Sungmook; Kim, Jumi (Expert systems with applications, 2012)
► 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.