Regularized LMS and diffusion adaptation LMS with graph filters for non-stationary data

In sensor networks, adaptive algorithms such as diffusion adaptation LMS are commonly used to learn and track non-stationary signals. When such signals have similarities across certain nodes as captured by a graph, then Laplacian Regularized (LR) LMS and diffusion adaptation LR LMS can be utilized for the respective centralized and distributed estimation cases. In this paper, we re-examine these adaptive methods, and use graph signal processing notions to augment the algorithms with an additional graph filtering step for regularization. Moreover, we demonstrate how to design these graph filters, leading to performance improvements over existing methods in both the centralized and distributed cases. Furthermore, we analyze the stability and convergence of our methods and illustrate how the empirical performance is captured by the theoretical results which unveil the bias and variance tradeoff.