Mean square convergence analysis for kernel least mean square algorithm

• Published in: Signal processing Vol. 92; no. 11; pp. 2624 - 2632
• Main Authors: Chen, Badong, Zhao, Songlin, Zhu, Pingping, Príncipe, José C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2012; Elsevier
• Subjects: Applied sciences; Computer simulation; Convergence; Detection, estimation, filtering, equalization, prediction; Energy conservation; Energy conservation relation; Exact sciences and technology; Information, signal and communications theory; Kernel adaptive filter; Kernel least mean square; Kernels; Least mean squares algorithm; Mean square convergence; Mean square values; Monte Carlo methods; Optimization; Signal and communications theory; Signal, noise; Telecommunications and information theory; Kernel adaptive filter; Kernel least mean square; Mean square convergence; Energy conservation relation; Monte Carlo method; Theoretical study; Adaptive filter; Algorithm; Steady state; Mean square error; Kernel method; Upper bound; Energy conservation; Signal processing; Numerical simulation; Least mean squares methods
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2012.04.007

In this paper, we study the mean square convergence of the kernel least mean square (KLMS). The fundamental energy conservation relation has been established in feature space. Starting from the energy conservation relation, we carry out the mean square convergence analysis and obtain several important theoretical results, including an upper bound on step size that guarantees the mean square convergence, the theoretical steady-state excess mean square error (EMSE), an optimal step size for the fastest convergence, and an optimal kernel size for the fastest initial convergence. Monte Carlo simulation results agree with the theoretical analysis very well. ► Mean-square convergence analysis for KLMS is carried out. ► An upper bound on step size is derived. ► Theoretical steady-state EMSE is obtained. ► Step size for the fastest convergence speed is derived. ► Kernel size for the fastest initial convergence is studied.