Adaptive Least Mean Squares Graph Neural Networks and Online Graph
  Signal Estimation
Yi Yan Changran Peng Ercan Engin Kuruoglu
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.