Robust logarithmic hyperbolic cosine adaptive filtering over graph signals

Abstract

Graph signal processing (GSP) has two methods including graph Fourier transform (GFT) and graph shift-operator (GSO) for dealing with the graph signal used for adaptive filtering (AF). However, in order to perform feature decomposition, GFT requires the availability of a band-limited graph signal with a known bandwidth in advance. Therefore, a general model based on GSO is then derived for AF by introducing a mixture coefficient to combine the advantages of different GSOs, comprehensively. Since the existing algorithms using the mean square error and other robust error criteria in GSP cannot effectively fight against non-Gaussian noises, a robust logarithmic hyperbolic cosine adaptive filter over graph (GLHCAF) algorithm is proposed by applying the logarithmic hyperbolic cosine loss function to the designed general model. The significant performance improvement of GLHCAF in non-Gaussian noises is obtained by simply controlling the scaling parameter. To avoid the parameter selections including scaling parameter and step size, the adaptive GLHCAF (AGLHCAF) algorithm is therefore proposed to further improve the performance of GLHCAF. Moreover, the mean square performance analysis of GLHCAF is given. Simulations in the real-world data are provided to assess the reliability and accuracy for theoretical analysis, the universality of the designed general model, and superiorities of proposed algorithms.