# Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation

arXiv: https://arxiv.org/abs/2401.15304 · HTML: https://mlsanity.com/paper/2401.15304/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 27 Jan 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [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)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [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)
- [Sequential Monte Carlo Graph Convolutional Network for Dynamic Brain Connectivity](https://mlsanity.com/paper/2310.00630/) (2023)
- [Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise](https://mlsanity.com/paper/2203.00320/) (2022)

## Built on by (most cited first, 1 of 1)

- [Adaptive Least Mean pth Power Graph Neural Networks](https://mlsanity.com/paper/2405.04111/) (2024)

## Abstract (arXiv)

The online prediction of multivariate signals, existing simultaneously in space and time, from noisy partial observations is a fundamental task in numerous applications. We propose an efficient Neural Network architecture for the online estimation of time-varying graph signals named the Adaptive Least Mean Squares Graph Neural Networks (LMS-GNN). LMS-GNN aims to capture the time variation and bridge the cross-space-time interactions under the condition that signals are corrupted by noise and missing values. The LMS-GNN is a combination of adaptive graph filters and Graph Neural Networks (GNN). At each time step, the forward propagation of LMS-GNN is similar to adaptive graph filters where the output is based on the error between the observation and the prediction similar to GNN. The filter coefficients are updated via backpropagation as in GNN. Experimenting on real-world temperature data reveals that our LMS-GNN achieves more accurate online predictions compared to graph-based methods like adaptive graph filters and graph convolutional neural networks.