Adaptive Least Mean pth Power Graph Neural Networks

• URL: http://arxiv.org/abs/2405.04111v2
• Date: Sat, 23 Nov 2024 10:26:22 GMT
• Title: Adaptive Least Mean pth Power Graph Neural Networks
• Authors: Yi Yan, Changran Peng, Ercan E. Kuruoglu,
• Abstract summary: We propose 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. 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.
• Score: 5.4004917284050835
• License:
• 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.

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