A Variable Parameter LMS Algorithm Based on Generalized Maximum Correntropy Criterion for Graph Signal Processing

The least mean square (LMS) algorithm of the graph signal processing (GSP) based on the mean square error criterion has a poor reconstruction effect when the graph sampling signal is disturbed by impulse noise. To solve this problem, the generalized maximum correntropy criterion (GMCC) is introduced, which is robust to impulse noise in adaptive filtering. Therefore, this paper proposes the GSP LMS algorithm based on the GMCC (GSP LMSGMCC) by using the graph Fourier transform, which has a good effect when the graph sampling signal is disturbed by impulse noise. In addition, the GSP LMSGMCC algorithm based on the fixed parameter including step size and kernel width must make a compromise between convergence speed and steady-state error. To prevent this, the fixed parameters of the proposed GSP LMSGMCC algorithm are optimized, respectively. To facilitate understanding and analysis, the steady-state performance of the proposed GSP LMSGMCC algorithm is studied. Finally, the computer simulations are carried out to verify the superiority of the proposed algorithm when the signals on the graph are static graph signals and streaming graph signals respectively.