This study introduces multivariate spatiotemporal Hawkes processes and network reconstruction.
In this paper, the authors develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. The results demonstrate that, in comparison to using only temporal data, the spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis---such as examinations of community structure and motifs---of the reconstructed networks. There is often latent network structure in spatial and temporal data, and the tools of network analysis can yield fascinating insights into such data. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, this approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. The authors illustrate their approach using both synthetic networks and networks that constructed from real-world data sets (a location-based social-media network, a narrative of crime events, and violent gang crimes). (Published Abstract Provided)