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Mathematical Problems in Engineering
Volume 2010, Article ID 378652, 16 pages
Research Article

Knowledge-Based Green's Kernel for Support Vector Regression

1Department of Electrical and Computer Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada M5B 2K3
2School of Information Technology Management, Ryerson University, Toronto, ON, Canada M5B 2K3

Received 19 January 2010; Accepted 19 May 2010

Academic Editor: Cristian Toma

Copyright © 2010 Tahir Farooq 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.


This paper presents a novel prior knowledge-based Green's kernel for support vector regression (SVR). After reviewing the correspondence between support vector kernels used in support vector machines (SVMs) and regularization operators used in regularization networks and the use of Green's function of their corresponding regularization operators to construct support vector kernels, a mathematical framework is presented to obtain the domain knowledge about magnitude of the Fourier transform of the function to be predicted and design a prior knowledge-based Green's kernel that exhibits optimal regularization properties by using the concept of matched filters. The matched filter behavior of the proposed kernel function makes it suitable for signals corrupted with noise that includes many real world systems. We conduct several experiments mostly using benchmark datasets to compare the performance of our proposed technique with the results already published in literature for other existing support vector kernel over a variety of settings including different noise levels, noise models, loss functions, and SVM variations. Experimental results indicate that knowledge-based Green's kernel could be seen as a good choice among the other candidate kernel functions.