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Adaptive Least Mean pth Power Graph Neural Networks

Yi Yan, Changran Peng, Ercan E. Kuruoglu

TL;DR

The Adaptive Least Mean Power Graph Neural Networks (LMP-GNN), a universal framework combining adaptive filter and graph neural network for online graph signal estimation, is proposed, which retains the advantage of adaptive filtering in handling noise and missing observations as well as the online update capability.

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.

Adaptive Least Mean pth Power Graph Neural Networks

TL;DR

The Adaptive Least Mean Power Graph Neural Networks (LMP-GNN), a universal framework combining adaptive filter and graph neural network for online graph signal estimation, is proposed, which retains the advantage of adaptive filtering in handling noise and missing observations as well as the online update capability.

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 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 -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.
Paper Structure (13 sections, 20 equations, 6 figures, 4 tables)

This paper contains 13 sections, 20 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Impulsive Distributions
  4. GSP Preliminaries
  5. Methodology
  6. Spectral Graph Neural Networks
  7. Adaptive Filtering
  8. Least Mean $p^{th}$ Power Graph Neural Network
  9. Special Cases of the LMP-GNN
  10. Experiments
  11. Experiment Setup
  12. Results and Discussion
  13. Conclusion

Figures (6)

  • Figure 1: An illustration of the temperature graph with time-varying temperature recordings at each weather station, displayed at three different time instances.
  • Figure 2: The probability density functions of various non-Gaussian distributions all with zero-mean/median (log scale).
  • Figure 3: A temperature graph with missing values and S$\alpha$S noise ($\alpha = 1.5$, $\gamma = 0.1$) on the time-varying temperature recordings at each weather station. The three displayed time instances are the same as in Figure \ref{['fig_ground_truth']}.
  • Figure 4: Restored time-varying temperature recordings from the missing and noisy observations using the LMP-GNN. The three displayed time instances are the same as in Figure \ref{['fig_ground_truth']}.
  • Figure 5: The MSE at each time instance of the temperature dataset under S$\alpha$S noise with $\alpha = 1.2$ and $\mu = 0.1$.
  • ...and 1 more figures