Kernel Adaptive Filtering Over Complex Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 35; no. 3; pp. 1 - 8
• Main Authors: Li, Wenling, Wang, Zidong, Hu, Jun, Du, Junping, Sheng, Weiguo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.03.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filters; Adaptive systems; Algorithms; Complex network; Complex networks; Convergence; Kernel; kernel adaptive filter; Learning systems; least mean square (LMS); Mathematical models; recursive least square (RLS); Upper bound; Upper bounds
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2022.3199679

This brief is concerned with the problem of kernel adaptive filtering for a complex network. First, a coupled kernel least mean square (KLMS) algorithm is developed for each node to uncover its nonlinear measurement function by using a series of input-output data. Subsequently, an upper bound is derived for the step-size of the coupled KLMS algorithm to guarantee the mean square convergence. It is shown that the upper bound is dependent on the coupling weights of the complex network. Especially, an optimal step size is obtained to achieve the fastest convergence speed and a suboptimal step size is presented for the purpose of practical implementations. Besides, a coupled kernel recursive least square (KRLS) algorithm is further proposed to improve the filtering performance. Finally, simulations are provided to verify the validity of the theoretical results.