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Mathematical Problems in Engineering
Volume 2013, Article ID 349120, 10 pages
http://dx.doi.org/10.1155/2013/349120
Research Article

Smooth Diagonal Weighted Newton Support Vector Machine

1School of Mathematical Sciences, Xi’an Shiyou University, Xi’an 710065, China
2School of Computer Sciences, Xidian University, Xi’an 710071, China

Received 8 August 2013; Accepted 27 October 2013

Academic Editor: Wei-Chiang Hong

Copyright © 2013 Jinjin Liang and De Wu. 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.

Abstract

Based on diagonal weighted support vector machine, a smooth model with Newton algorithm is proposed and is called SDWNSVM for short. SDWNSVM introduces the entropy function to approximate the plus function of the slack in the diagonal weighted SVM and is thus different from traditional SSVM that treats a reformulation problem. SDWNSVM utilizes the dual technique to rewrite the objection function by the connotative relation between the primal and dual program, which induces an exact smooth program and differs from traditional SSVM that uses Lagrangian multipliers to roughly substitute for the hyperplane weight. SDWNSVM proves the equivalence between the obtained model and the original one and proposes Newton algorithm to figure out the optimal solution. Numerical experiments on UCI data demonstrate that SDWNSVM has higher accuracies and less iteration than existing methods.