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Volume 2017, Article ID 2691474, 14 pages
Research Article

Kernel Negative ε Dragging Linear Regression for Pattern Classification

Yali Peng,1,2,3 Lu Zhang,1,2 Shigang Liu,1,2,3 Xili Wang,1,2 and Min Guo2,3

1Key Laboratory of Modern Teaching Technology, Ministry of Education, Xi’an 710062, China
2Engineering Laboratory of Teaching Information Technology of Shaanxi Province, Xi’an 710119, China
3School of Computer Science, Shaanxi Normal University, Xi’an 710119, China

Correspondence should be addressed to Shigang Liu; nc.ude.unns@uilghs

Received 27 August 2017; Accepted 9 November 2017; Published 10 December 2017

Academic Editor: Chuan Zhou

Copyright © 2017 Yali Peng 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.


Linear regression (LR) and its variants have been widely used for classification problems. However, they usually predefine a strict binary label matrix which has no freedom to fit the samples. In addition, they cannot deal with complex real-world applications such as the case of face recognition where samples may not be linearly separable owing to varying poses, expressions, and illumination conditions. Therefore, in this paper, we propose the kernel negative dragging linear regression (KNDLR) method for robust classification on noised and nonlinear data. First, a technique called negative dragging is introduced for relaxing class labels and is integrated into the LR model for classification to properly treat the class margin of conventional linear regressions for obtaining robust result. Then, the data is implicitly mapped into a high dimensional kernel space by using the nonlinear mapping determined by a kernel function to make the data more linearly separable. Finally, our obtained KNDLR method is able to partially alleviate the problem of overfitting and can perform classification well for noised and deformable data. Experimental results show that the KNDLR classification algorithm obtains greater generalization performance and leads to better robust classification decision.