Study of Set-Membership Kernel Adaptive Algorithms and Applications
This work addresses computational efficiency for researchers and practitioners using kernel adaptive algorithms, but it is incremental as it builds on established methods.
The authors tackled the problem of growing dictionary size in kernel adaptive algorithms by deriving set-membership kernel-based normalized least-mean square (SM-NKLMS) and kernelized affine projection (SM-KAP) algorithms to limit dictionary size in stationary environments, with experiments comparing them to existing methods.
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.