Generalized Hermite kernel function for support vector machine classifications

摘要

Support vector machines (SVMs) have proved to be promising methods for classification and regression analysis because of their solid mathematical foundations which convey several salient properties that other methods hardly provide. The critical SVMs problem is to select appropriate kernels as the performance of SVMs depends on this choice. In this paper, a set of new Hermite kernel functions is proposed for accurate SVMs classification. Besides clarifying how to apply the proposed Hermite kernel functions on vector inputs, we also enhanced the generalization capability of the proposed method when applied to a variety of classification problems. The generalized kernel functions are induced from Hermite polynomials which proved orthogonality and recurrence. The proposed generalized Hermite kernels satisfy Mercer's condition and are stated in the general form, allowing us to derive different kernel functions. The accuracy of the proposed kernels is compared with that of the existing kernels such as Universal, Chebyshev, Gaussian, and Polynomial by applying them to a variety of non-separable data sets with several attributes. It is shown that the proposed kernel gives good classification accuracy in nearly all the data sets, especially those of high dimensions.