  The crime forecasting is an important problem as it greatly contributes to
urban safety. Typically, the goal of the problem is to predict different types
of crimes for each geographical region (like a neighborhood or censor tract) in
the near future. Since nearby regions usually have similar socioeconomic
characteristics which indicate similar crime patterns, recent state-of-the-art
solutions constructed a distance-based region graph and utilized Graph Neural
Network (GNN) techniques for crime forecasting, because the GNN techniques
could effectively exploit the latent relationships between neighboring region
nodes in the graph. However, this distance-based pre-defined graph cannot fully
capture crime correlation between regions that are far from each other but
share similar crime patterns. Hence, to make an accurate crime prediction, the
main challenge is to learn a better graph that reveals the dependencies between
regions in crime occurrences and meanwhile captures the temporal patterns from
historical crime records. To address these challenges, we propose an end-to-end
graph convolutional recurrent network called HAGEN with several novel designs
for crime prediction. Specifically, our framework could jointly capture the
crime correlation between regions and the temporal crime dynamics by combining
an adaptive region graph learning module with the Diffusion Convolution Gated
Recurrent Unit (DCGRU). Based on the homophily assumption of GNN, we propose a
homophily-aware constraint to regularize the optimization of the region graph
so that neighboring region nodes on the learned graph share similar crime
patterns, thus fitting the mechanism of diffusion convolution. It also
incorporates crime embedding to model the interdependencies between regions and
crime categories. Empirical experiments and comprehensive analysis on two
real-world datasets showcase the effectiveness of HAGEN.
