An adaptive support vector regression based on a new sequence of unified orthogonal polynomials

Authors:
Jinwei Zhao;Guirong Yan;Boqin Feng;Wentao Mao;Junqing Bai
Affiliations:
Department of Computer Science, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China;State Key Laboratory of Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China;Department of Computer Science, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China;College of Computer and Information Technology, Henan Normal University, Xinxiang 453007, China;State Key Laboratory of Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
Venue:
Pattern Recognition
Year:
2013

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Abstract

In practical engineering, small-scale data sets are usually sparse and contaminated by noise. In this paper, we propose a new sequence of orthogonal polynomials varying with their coefficient, unified Chebyshev polynomials (UCP), which has two important properties, namely, orthogonality and adaptivity. Based on these new polynomials, a new kernel function, the unified Chebyshev kernel (UCK), is constructed, which has been proven to be a valid SVM kernel. To find the optimal polynomial coefficient and the optimal kernel, we propose an adaptive algorithm based on the evaluation criterion for adaptive ability of UCK. To evaluate the performance of the new method, we applied it to learning some benchmark data sets for regression, and compared it with other three algorithms. The experiment results show that the proposed adaptive algorithm has excellent generalization performance and prediction accuracy, and does not cost more time compared with other SVMs. Therefore, this method is suitable for practical engineering application.