Analysis of legendre polynomial kernel in support vector machines

Abstract

For several types of machines learning problems, the support vector machine is a method of choice. The kernel functions are a basic ingredient in support vector machine theory. Kernels based on the concepts of orthogonal polynomials gave the great satisfaction in practice. In this paper we identify the reproducing kernel Hilbert space of legendre polynomial kernel which allows us to understand its ability to extract more discriminative features. We also show that without being a universal kernel, legendre kernel possesses the same separation properties. The legendre, Gaussian and polynomial kernel performance has been first evaluated on two dimensional illustrative examples in order to give a graphical comparison, then on real world data sets from UCI repository. For nonlinearly separable data, legendre kernel always gives satisfaction regarding classification accuracy and reduction in the number of support vectors.