Spline function smooth support vector machine for classification

Yubo Yuan; Weiguo Fan; Dongmei Pu

doi:10.3934/jimo.2007.3.529

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2007, Volume 3, Issue 3: 529-542. Doi: 10.3934/jimo.2007.3.529

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Spline function smooth support vector machine for classification

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

Received: August 31, 2006

Revised: April 30, 2007

Published: June 2007

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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.

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Mathematics Subject Classification: Primary: 90C20; Secondary: 65L07; 65N12.

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