  Time series forecasting and spatiotemporal kriging are the two most important
tasks in spatiotemporal data analysis. Recent research on graph neural networks
has made substantial progress in time series forecasting, while little
attention has been paid to the kriging problem -- recovering signals for
unsampled locations/sensors. Most existing scalable kriging methods (e.g.,
matrix/tensor completion) are transductive, and thus full retraining is
required when we have a new sensor to interpolate. In this paper, we develop an
Inductive Graph Neural Network Kriging (IGNNK) model to recover data for
unsampled sensors on a network/graph structure. To generalize the effect of
distance and reachability, we generate random subgraphs as samples and
reconstruct the corresponding adjacency matrix for each sample. By
reconstructing all signals on each sample subgraph, IGNNK can effectively learn
the spatial message passing mechanism. Empirical results on several real-world
spatiotemporal datasets demonstrate the effectiveness of our model. In
addition, we also find that the learned model can be successfully transferred
to the same type of kriging tasks on an unseen dataset. Our results show that:
1) GNN is an efficient and effective tool for spatial kriging; 2) inductive
GNNs can be trained using dynamic adjacency matrices; 3) a trained model can be
transferred to new graph structures and 4) IGNNK can be used to generate
virtual sensors.
