The Online Random Fourier Features Conjugate Gradient Algorithm

Abstract

Kernel conjugate gradient (KCG) algorithms have been proposed to improve the convergence rate and filtering accuracy of kernel adaptive filters (KAFs). However, sparsification is still required in the KCG algorithms to curb the growth of network structure for online applications. To address this issue, a novel online random Fourier features conjugate gradient (RFFCG) algorithm based on the minimum mean-square error criterion is proposed by approximating the kernel with the random Fourier features. With no requirement of sparsification, the proposed RFFCG significantly reduces the computational and storage complexities in KAFs. Meanwhile, the RFFCG efficiently uses only one error in the loss function to approach the filtering accuracy of the KAF with sparsification based on all the errors in the loss function. Monte Carlo simulations on short-term chaotic time-series prediction validate the superiorities of the proposed RFFCG algorithm.