Chebyshev kernel with orthogonal features

Kernel methods play important roles in machine learning algorithms such as support vector machines. However, how to construct a suitable kernel remains difficult. Recently Ye et al proposed a new kind of kernel function named Chebyshev kernel based on orthogonal Chebyshev polynomials. But in fact the features of the nonlinear mapping determined by Chebyshev kernel are not orthogonal to each other due to the denominator in Chebyshev kernel. Thus we propose a new kernel named orthogonal Chebyshev kernel which determines a nonlinear mapping with orthogonal features. We prove that it is a valid kernel. Experimental results in both classification and regression tasks show that orthogonal Chebyshev kernel is effective and competitive to Chebyshev kernel.