Support vector machine with orthogonal Legendre kernel

Support vector machines (SVMs) are probably the most well-known models based on kernel substitution. Based on orthogonal Legendre polynomials, an orthogonal Legendre kernel function for support vector machine is proposed using the properties of kernel functions. We then prove that it satisfies the Mercer condition. Compared to traditional kernel functions such as polynomial or gaussian kernels, orthogonal Legendre kernel can reduce the redundancy in feature space due to the orthogonality of Legendre polynomials, which may enable the S VM to construct the separating hyperplane with less support vectors. Compared to orthogonal Chebyshev kernel function, orthogonal Legendre kernel is faster and saves more time. Experimental results show that orthogonal Legendre kernel is competitive to other kernel functions.