Multiple recursive projection twin support vector machine for multi-class classification
- PDF / 843,286 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 3 Downloads / 188 Views
ORIGINAL ARTICLE
Multiple recursive projection twin support vector machine for multi-class classification Chun-Na Li • Yun-Feng Huang • He-Ji Wu Yuan-Hai Shao • Zhi-Min Yang
•
Received: 20 March 2014 / Accepted: 23 July 2014 Ó Springer-Verlag Berlin Heidelberg 2014
Abstract For multi-class classification problem, a novel multiple projection twin support vector machine (MultiPTSVM) is proposed. Our Multi-PTSVM solves K quadratic programming problems (QPPs) to obtain K projection axes, which is similar to binary PTSVM, but the regularization terms and recursive procedure are introduced for each class, which improve the generalization ability greatly. Comparisons against the Multi-SVM, Multi-TWSVM, Multi-GEPSVM, and our Multi-PTSVM on both synthetic and benchmark datasets indicate that our Multi-PTSVM has its advantages. Keywords Multi-class classification Multiple recursive projection Twin support vector machine Projection twin support vector machine
C.-N. Li Y.-H. Shao (&) Z.-M. Yang Zhijiang College, Zhejiang University of Technology, Hangzhou 310024, People’s Republic of China e-mail: [email protected] C.-N. Li e-mail: [email protected] Z.-M. Yang e-mail: [email protected] Y.-F. Huang Hangzhou Navigation Instrument Company Limited and Institute of special equipment, Zhejiang University of Technology, Hangzhou, People’s Republic of China H.-J. Wu College of Science, Zhejiang University of Technology, Hangzhou 310024, People’s Republic of China e-mail: [email protected]
1 Introduction In recently, the nonparallel support vector machines have attracted wildly attentions, and many nonparallel hyperplane classifiers were proposed for binary classification. For example, Mangasarian and Wild [15] proposed the first nonparallel hyperplane classifier named as generalized eigenvalue proximal support vector machine (GEPSVM), whose goal is to find two nonparallel hyperplanes such that each hyperplane is closets to one of the two classes and as far as possible from the other class. Since its excellent performance especially when dealing with the ‘‘Cross Plances’’ datasets comparing to classical support vector machine (SVM) [1, 8, 9, 31, 35, 36], various generalizations are proposed as improvement of GEPSVM [2, 6, 11, 23, 24, 26, 34, 39]. Shao et al. [27] improved GEPSVM by replacing the two general eigenvalue problems by two simple eigenvalues problems, and avoided the singular problems possibly appeared in GEPSVM. From another point of view, Jayadeva et al. [12] proposed a twin support vector machine (TWSVM) classifier which also aims at generating two nonparallel hyperplanes such that each hyperplane is closer to one of the two classes and is as far as possible from the other, but with the different formulation such that TWSVM solves a pair of SVM-type QPPs, while GEPSVM solves two generalized eigenvalue problems. As a powerful classification tool, many authors have improved TWSVM from different aspects [13, 17–19, 22, 25, 30, 33]. On the other hand, the hyperplanes constructed by GEPSVM also have been extend
Data Loading...
