Study of Set-Membership Kernel Adaptive Algorithms and Applications

TL;DR

This paper introduces set-membership kernel adaptive algorithms, specifically SM-NKLMS and SM-KAP, which control dictionary size in nonlinear adaptive filtering, demonstrated through comparative experiments.

Contribution

The paper develops novel set-membership kernel adaptive algorithms that effectively limit dictionary growth in stationary environments, enhancing efficiency.

Findings

SM-NKLMS effectively limits dictionary size.

SM-KAP improves convergence in nonlinear scenarios.

Experimental results show competitive performance with existing methods.

Abstract

Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with nonlinearities. Nevertheless these methods deal with kernel expansions, creating a growing structure also known as dictionary, whose size depends on the number of new inputs. In this paper we derive the set-membership kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is capable of limiting the size of the dictionary created in stationary environments. We also derive as an extension the set-membership kernelized affine projection (SM-KAP) algorithm. Finally several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to the existing methods.