Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation
This addresses the need for efficient online signal estimation in applications like sensor networks, though it is incremental as it builds on prior graph-based techniques.
The paper tackles the problem of online prediction of time-varying graph signals from noisy partial observations by proposing LMS-GNN, which combines adaptive graph filters and Graph Neural Networks, and achieves more accurate predictions on real-world temperature data compared to existing graph-based methods.
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.