# American Institute of Mathematical Sciences

July  2007, 3(3): 529-542. doi: 10.3934/jimo.2007.3.529

## Spline function smooth support vector machine for classification

 1 School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China, China 2 Accounting & Information Systems, Virginia Polytechnic Institute and State University, VA, 24061, United States

Received  September 2006 Revised  May 2007 Published  July 2007

Support vector machine (SVM) is a very popular method for binary data classification in data mining (machine learning). Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of good optimal algorithms can't be used to find the solution. In order to overcome this model's non-smooth property, Lee and Mangasarian proposed smooth support vector machine (SSVM) in 2001. Later, Yuan et al. proposed the polynomial smooth support vector machine (PSSVM) in 2005. In this paper, a three-order spline function is used to smooth the objective function and a three-order spline smooth support vector machine model (TSSVM) is obtained. By analyzing the performance of the smooth function, the smooth precision has been improved obviously. Moreover, BFGS and Newton-Armijo algorithms are used to solve the TSSVM model. Our experimental results prove that the TSSVM model has better classification performance than other competitive baselines.
Citation: Yubo Yuan, Weiguo Fan, Dongmei Pu. Spline function smooth support vector machine for classification. Journal of Industrial & Management Optimization, 2007, 3 (3) : 529-542. doi: 10.3934/jimo.2007.3.529
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