Temporal Network Kernel Density Estimation

Kernel density estimation (KDE) is a widely used method in geography to study concentration of point pattern data. Geographical networks are 1.5 dimensional spaces with specific characteristics, analyzing events occurring on networks (accidents on roads, leakages of pipes, species along rivers, etc.). In the last decade, they required the extension of spatial KDE. Several versions of Network KDE (NKDE) have been proposed, each with their particular advantages and disadvantages, and are now used on a regular basis. However, scant attention has been given to the temporal extension of NKDE (TNKDE). In practice, when the studied events happen at specific time points and are constrained on a network, the methodologies used by geographers tend to overlook either the network or the temporal dimension. Here we propose a TNKDE based on the recent development of NKDE and the product of kernels. We also adapt classical methods of KDE (Diggle's correction, Abramson's adaptive bandwidth and bandwidth selection by leave-one-out maximum likelihood). We also illustrate the method with Montreal road crashes involving a pedestrian between 2016 and 2019.