Multikernel adaptive filtering based on random features approximation

Abstract

Multikernel adaptive filters (MKAFs) have been proposed to address the selection issue of kernel parameter in single kernel based kernel adaptive filters (KAFs). However, the conventional MKAFs suffer from large memory requirements and computational burdens owing to their growing network structures. To address this issue, a random features approximation for online multikernel adaptive filtering is presented in this paper. Based on this efficient approximation, a novel robust MKAF based on the minimum kernel mean p-power error criterion, namely multiple random features kernel mean p-power (MRFKMP) algorithm, is therefore proposed in a fixed-dimensional random Fourier features space. The mean square steady-state performance of MRFKMP is derived for theoretical analysis in terms of excess mean square error (EMSE). In addition, an extension of MRFKMP is further developed in a recursive form for performance improvement. Monte Carlo simulations are conducted to validate the obtained theoretical results and the superiorities of the proposed algorithms from the aspects of computational efficiency, filtering accuracy, robustness to large outliers.