Modelling of chaotic systems using wavelet kernel partial least squares regression method

Abstract

Based on the powerful nonlinear mapping ability of kernel learning, and in combination with the partial least square (PLS) algorithm for linear regression, a wavelet kernel partial least square (WKPLS) regression method is proposed. By the method, the input-output data are firstly mapped to a nonlinear higher dimensional feature space, a linear PLS regression model is then constructed by the classic kernel transformation trick used in support vector machines. The PLS approach utilizes the covariance between input and output variables to extract latent features, and the wavelet kernel which is an admissible support vector kernel function is characterized by its local analysis and approximate orthogonality. Hence, the proposed WKPLS method combining PLS approach with wavelet kernel function shows excellent learning performance for modeling nonlinear dynamic systems. The WKPLS is then applied to modelling of several chaotic dynamical systems and compared with the kernel partial least squares(KPLS) method using Gaussian kernel function. Simulation results confirm that the WKPLS identifier is fast and can accurately approximate unknown chaotic dynamical system, and its approximation accuracy is higher than the KPLS under the same conditions.