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Mathematical Problems in Engineering
Volume 2013, Article ID 135149, 7 pages
Research Article

Piecewise-Smooth Support Vector Machine for Classification

School of Automation, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

Received 18 November 2012; Revised 12 March 2013; Accepted 13 March 2013

Academic Editor: Jun Zhao

Copyright © 2013 Qing Wu and Wenqing Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Support vector machine (SVM) has been applied very successfully in a variety of classification systems. We attempt to solve the primal programming problems of SVM by converting them into smooth unconstrained minimization problems. In this paper, a new twice continuously differentiable piecewise-smooth function is proposed to approximate the plus function, and it issues a piecewise-smooth support vector machine (PWSSVM). The novel method can efficiently handle large-scale and high dimensional problems. The theoretical analysis demonstrates its advantages in efficiency and precision over other smooth functions. PWSSVM is solved using the fast Newton-Armijo algorithm. Experimental results are given to show the training speed and classification performance of our approach.