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.

我们提出了一种用于在线估计时变图信号的高效神经网络架构，名为自适应最小均方图神经网络（LMS-GNN），它旨在捕捉时间变化和填补受噪声和缺失值影响的信号的空间和时间跨度相互作用，通过自适应图滤波器和图神经网络的组合实现。实验表明，与自适应图滤波器和图卷积神经网络等基于图的方法相比，我们的 LMS-GNN 实现了更准确的在线预测。