Modified matrix splitting method for the support vector machine and its application to the credit classification of companies in Korea

Authors:
Gitae Kim;Chih-Hang Wu;Sungmook Lim;Jumi Kim
Affiliations:
Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2033 Durland Hall, Manhattan, KS 66506, USA;Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2018 Durland Hall, Manhattan, KS 66506, USA;Division of Business Administration, Korea University, Jochiwon-Eup, Yeongi-Gun, Chungnam 339-700, Republic of Korea;Korea Small Business Institute (KOSBI), 16-2 Yoido-dong, Yeongdeungpo-ku, Seoul 150-742, Republic of Korea
Venue:
Expert Systems with Applications: An International Journal
Year:
2012

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Abstract

This research proposes a solving approach for the @n-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 @n-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.