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Journal of Industrial and Management Optimization (JIMO)
 

Spline function smooth support vector machine for classification

Pages: 529 - 542, Volume 3, Issue 3, August 2007

doi:10.3934/jimo.2007.3.529       Abstract        Full Text (180.8K)       Related Articles

Yubo Yuan - School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China (email)
Weiguo Fan - Accounting & Information Systems, Virginia Polytechnic Institute and State University, VA, 24061, United States (email)
Dongmei Pu - School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China (email)

Abstract: 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.

Keywords:  Quadratic Programming, Data Mining,Support Vector Machine.
Mathematics Subject Classification:  Primary: 90C20; Secondary: 65L07; 65N12.

Received: September 2006;      Revised: May 2007;      Published: July 2007.