Deep Learning-Based Robust Adaptive Algorithm for Graph Signal Estimation With Trainable Parameters

The adaptive algorithm used for graph signal processing (GSP) based on the least mean square (LMS) strategy has poor performance in impulse noise environment, while the generalized maximum correntropy criterion (GMCC)-based GSP LMS (GSP LMSGMCC) algorithm effectively solves the mentioned above problem and is applicable to Gaussian noise scenarios. However, the manual debugging process of the step size, kernel parameter and shape parameter of the GSP LMSGMCC algorithm is complex, and inappropriate parameters can adversely affect its performance. Moreover, the variable step size (VSS) and variable kernel width (VKW) versions of the GSP LMSGMCC algorithm has more complex parameters that need to be debugged. To solve the mentioned problems, based on deep learning, we extend the iterative formulation of the GSP LMSGMCC algorithm to a multilayer neural network with the mentioned three parameters trainable. The neural network is trained on a dataset constructed based on the Brazilian temperature dataset. Simulation results show that our proposed method not only circumvents the manual selection of the related parameters, but also achieves a better coordination between the steady-state error accuracy and convergence rate.