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The Scientific World Journal
Volume 2015, Article ID 497617, 12 pages
http://dx.doi.org/10.1155/2015/497617
Research Article

A Learning Framework of Nonparallel Hyperplanes Classifier

1College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
2State Key Lab of Biochemical Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
3Zhijiang College, Zhejiang University of Technology, Hangzhou 310024, China

Received 21 June 2014; Revised 19 September 2014; Accepted 19 September 2014

Academic Editor: Qiankun Song

Copyright © 2015 Zhi-Xia Yang et al. 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

A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM’s deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value , which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization.