A novel support vector machine method for classification is presented in this paper. A modified kernel function based on the similarity metric and Riemannian metric is applied to the support vector machine. In general, it is believed that the similarity of homogeneous samples is higher than that of inhomogeneous samples. Therefore, in Riemannian geometry, Riemannian metric can be used to reflect local property of a curve. In order to enlarge the similarity metric of the homogeneous samples or reduce that of the inhomogeneous samples in the feature space, Riemannian metric is used in the kernel function of the SVM. Simulated experiments are performed using the databases including an artificial and the UCI real data. Simulation results show the effectiveness of the proposed algorithm through the comparison with four typical kernel functions without similarity metric.

support vector machine, Riemannian metric, similarity metric