Adaptive Least Mean pth Power Graph Neural Networks

TL;DR

This paper introduces LMP-GNN, a novel adaptive graph neural network framework that effectively predicts time-varying graph signals in noisy and incomplete data environments, improving robustness and accuracy.

Contribution

It presents a universal adaptive filtering framework with online trainable graph neural networks, incorporating $l_p$-norm optimization for robust estimation in impulsive noise conditions.

Findings

LMP-GNN outperforms existing methods in accuracy and robustness.

The Sign-GNN variant provides a simplified yet effective approach.

Experimental results on real datasets validate the method's effectiveness.

Abstract

In the presence of impulsive noise, and missing observations, accurate online prediction of time-varying graph signals poses a crucial challenge in numerous application domains. We propose the Adaptive Least Mean $p^{th}$ Power Graph Neural Networks (LMP-GNN), a universal framework combining adaptive filter and graph neural network for online graph signal estimation. LMP-GNN retains the advantage of adaptive filtering in handling noise and missing observations as well as the online update capability. The incorporated graph neural network within the LMP-GNN can train and update filter parameters online instead of predefined filter parameters in previous methods, outputting more accurate prediction results. The adaptive update scheme of the LMP-GNN follows the solution of a $l_p$-norm optimization, rooting to the minimum dispersion criterion, and yields robust estimation results for time-varying graph signals under impulsive noise. A special case of LMP-GNN named the Sign-GNN is also provided and analyzed, Experiment results on two real-world datasets of temperature graph and traffic graph under four different noise distributions prove the effectiveness and robustness of our proposed LMP-GNN.