A kernel least mean square algorithm based on randomized feature networks

To construct an online kernel adaptive filter in a non-stationary environment, we propose a randomized feature networks-based kernel least mean square (KLMS-RFN) algorithm. In contrast to the Gaussian kernel, which implicitly maps the input to an infinite dimensional space in theory, the randomized feature mapping transform inputs samples into a relatively low-dimensional feature space, where the transformed samples are approximately equivalent to those in the feature space using a shift-invariant kernel. The mean square convergence process of the proposed algorithm is investigated under the uniform convergence analysis method of a nonlinear adaptive filter. The computational complexity is also evaluated. In Lorenz time series prediction and nonstationary channel equalization scenarios, the simulation results demonstrate the effectiveness of the proposed algorithm.