# Adaptive Least Mean pth Power Graph Neural Networks

arXiv: https://arxiv.org/abs/2405.04111 · HTML: https://mlsanity.com/paper/2405.04111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Adaptive Least Mean Squares Estimation of Graph Signals](https://mlsanity.com/paper/1602.05703/) (2016)
- [Adaptive Sign Algorithm for Graph Signal Processing](https://mlsanity.com/paper/2201.05821/) (2022)
- [Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies](https://mlsanity.com/paper/1709.03726/) (2017)
- [Sequential Monte Carlo Graph Convolutional Network for Dynamic Brain Connectivity](https://mlsanity.com/paper/2310.00630/) (2023)
- [Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation](https://mlsanity.com/paper/2401.15304/) (2024)

## Abstract (arXiv)

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 pth 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 lp-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.