Adaptive Random Fourier Features Kernel LMS

TL;DR

The paper introduces an adaptive kernel LMS algorithm that dynamically adjusts the kernel bandwidth using random Fourier features, enhancing tracking and convergence in non-stationary environments.

Contribution

It presents a novel adaptive kernel LMS method that optimizes the kernel bandwidth online, improving performance over fixed-bandwidth kernel filters.

Findings

Improved convergence rate compared to fixed-bandwidth filters.

Enhanced steady-state error performance.

Better tracking ability in non-stationary scenarios.

Abstract

We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation cost. However, as an extra flexibility, it can adapt the inherent kernel bandwidth in the random Fourier features in an online manner. This adaptation mechanism allows to alleviate the problem of selecting the kernel bandwidth beforehand for the benefit of an improved tracking in non-stationary circumstances. Simulation results confirm that the proposed algorithm achieves a performance improvement in terms of convergence rate, error at steady-state and tracking ability over other kernel adaptive filters with preset kernel bandwidth.