[Paper Review] Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

Baichuan Yuan, Hao Li+3 more|arXiv (Cornell University)|Nov 15, 2018

Diffusion and Search DynamicsBiochemistry, Genetics and Molecular Biology57 references3 citations

TL;DR

This paper proposes a nonparametric method for reconstructing latent networks from spatiotemporal point processes using multivariate Hawkes processes that jointly model temporal and spatial dependencies. By leveraging both event timing and location, the approach improves network reconstruction accuracy over purely temporal methods, as demonstrated on synthetic data and real-world datasets including social media check-ins and crime events.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of inferring latent network structures from incomplete or unobserved relational data in spatiotemporal systems.
• To develop a method that integrates both spatial and temporal information in network reconstruction, overcoming limitations of purely temporal models.
• To enable nonparametric estimation of network dynamics without assuming a specific parametric form for triggering kernels or edge weights.
• To improve the accuracy of network reconstruction for downstream analyses such as community detection and motif analysis.
• To validate the method on diverse real-world datasets, including social media check-ins and crime event sequences.

Proposed method

• Models observed events as a multivariate Hawkes process where each event is associated with a spatiotemporal point (time, location, and entity).
• Uses a nonparametric kernel-based estimation of the triggering kernel to capture general temporal and spatial dependencies between events.
• Applies an expectation-maximization (EM)-type algorithm to infer the underlying network structure from event data.
• Estimates pairwise interaction strengths (network edges) based on the likelihood of one event triggering another, using both inter-event time and spatial distance.
• Incorporates spatial distance as a covariate in the triggering kernel, allowing for nonparametric estimation of how proximity affects influence.
• Performs network reconstruction by maximizing the likelihood of observed event sequences under the multivariate Hawkes model with spatial-temporal dependence.

Experimental results

Research questions

• RQ1 Can joint modeling of temporal and spatial dependencies improve network reconstruction accuracy compared to purely temporal models?
• RQ2 How well can a nonparametric Hawkes process recover latent network structure when the true network dynamics are unknown or complex?
• RQ3 To what extent does incorporating spatial proximity enhance the detection of causal interactions in event sequences?
• RQ4 How does the method perform on real-world datasets with varying network topologies and data sparsity?
• RQ5 Can the reconstructed networks support meaningful downstream analyses such as community detection and motif identification?

Key findings

• The spatiotemporal approach significantly improves network reconstruction accuracy compared to purely temporal methods on both synthetic and real-world datasets.
• On the Gowalla NYC dataset, the method achieved accurate reconstruction on a reduced network of 46 users and 8,495 check-ins, with improved edge recovery over temporal-only baselines.
• For the Los Angeles dataset, the method successfully reconstructed a network of 23 users and 6,203 check-ins, demonstrating robustness on smaller, sparser networks.
• The 1-ego network in San Francisco (9,887 check-ins) showed that the method can recover meaningful interaction patterns even in localized, ego-centered networks.
• Reconstructed networks enabled effective community detection and motif analysis, validating the utility of the inferred structure for further network science applications.
• The method demonstrated nonparametric flexibility by capturing complex, data-driven dependencies between spatial proximity and triggering intensity without assuming parametric forms.