  Spatiotemporal data can be represented as a process over a graph, which
captures their spatial relationships either explicitly or implicitly. How to
leverage such a structure for learning representations is one of the key
challenges when working with graphs. In this paper, we represent the
spatiotemporal relationships through product graphs and develop a first
principle graph-time convolutional neural network (GTCNN). The GTCNN is a
compositional architecture with each layer comprising a graph-time
convolutional module, a graph-time pooling module, and a nonlinearity. We
develop a graph-time convolutional filter by following the shift-and-sum
principles of the convolutional operator to learn higher-level features over
the product graph. The product graph itself is parametric so that we can learn
also the spatiotemporal coupling from data. We develop a zero-pad pooling that
preserves the spatial graph (the prior about the data) while reducing the
number of active nodes and the parameters. Experimental results with synthetic
and real data corroborate the different components and compare with baseline
and state-of-the-art solutions.
