Kernel Least Mean Kurtosis Based Online Chaotic Time Series Prediction

Based on the kernel methods and the nonlinear feature of chaotic time series, we develop a new algorithm called kernel least mean kurtosis (KLMK) by applying the kernel trick to the least mean kurtosis (LMK) algorithm, which maps the input data to a high dimensional feature space. The KLMK algorithm can overcome the shortcomings of the original LMK for nonlinear time series prediction, and it is easy to implement a sample by sample adaptation procedure. Theoretical analysis suggests that the KLMK algorithm may converge in a mean square sense in nonlinear chaotic time series prediction under certain conditions. Simulation results show that the performance of KLMK is better than those of LMK and the kernel least mean square (KLMS) algorithm.