Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

• Main Authors: Yuan, Baichuan, Li, Hao, Bertozzi, Andrea L, Brantingham, P. Jeffrey, Porter, Mason A
• Format: Journal Article
• Language: English
• Published: 15.11.2018
• Subjects: Computer Science - Social and Information Networks; Physics - Adaptation and Self-Organizing Systems; Physics - Physics and Society; Statistics - Machine Learning
• DOI: 10.48550/arxiv.1811.06321

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 this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our 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. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks.