Adaptive Least Mean pth Power Graph Neural Networks
<|reference_start|>Adaptive Least Mean pth Power Graph Neural Networks: 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.<|reference_end|>
@article{peng2024adaptive,
    title={Adaptive Least Mean pth Power Graph Neural Networks},
    author={Changran Peng, Yi Yan, Ercan E. Kuruoglu},
    journal={arXiv preprint arXiv:2405.04111},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.04111},
    primaryClass={cs.LG eess.SP}
}