Distributed Nonlinear Polynomial Adaptive Graph Filter Based on Diffusion Conjugate Gradient Strategy

This brief investigates distributed and adaptive estimation of streaming data based nonlinear graph filters. To begin with, a new distributed polynomial filter for nonlinear graphs is proposed based on the Hadamard product, which not only represents the nonlinear relationship between dynamically changing graph input and output signals, but also accounts for the time dimension. A diffusion least mean square algorithm is presented to estimate the nonlinear polynomial graph filter parameters in a distributed manner. The method of diffusion hybrid conjugate gradient is leveraged to further improve the convergence rate of the graph diffusion adaptive filter. The advantages of the proposed algorithms are demonstrated in simulation studies.