Knowledge-Based Green's Kernel for Support Vector Regression

Abstract

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.