Reproducing Kernel Function Based on Walsh Series

A new reproducing kernel function of least square support vector machines based on Walsh series is presented in this paper. The reproducing kernel is constructed in reproducing kernel Hilbert space (RKHS). Because the Hilbert space and the square integrable space are isomorphic, according to the wavelet multi-resolution analysis, Walsh consequence can be seen a set of orthogonal basis to construct the reproducing kernel. The simulation results are discussed to illustrate the proposed method.