Spectral clustering for dependent community Hawkes process models of temporal networks

2025-05-28

AI Summary

Modeling continuous-time networks (e.g., social interactions, financial transactions) poses challenges due to mutually exciting dependencies between node pairs—where one event increases the intensity of subsequent events elsewhere—and dynamically evolving community structures. Method: This paper proposes the Dependent Community Hawkes (DCH) model—the first generative joint model coupling the stochastic block model with a multivariate Hawkes process, enabling falsifiable inference of time-varying communities and excitation dynamics. Contributions/Results: Theoretically, we derive a non-asymptotic upper bound on spectral clustering error applied to the event count matrix, explicitly characterizing its dependence on node count, number of communities, observation duration, and excitation strength. Methodologically, we design a lightweight DCH variant—retaining only self- and cross-excitation terms—and a consistent Generalized Method of Moments (GMM) estimator, proving its statistical consistency under joint growth of network size and observation time. The resulting algorithm combines rigorous theoretical guarantees with high scalability.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Temporal networks observed continuously over time through timestamped relational events data are commonly encountered in application settings including online social media communications, financial transactions, and international relations. Temporal networks often exhibit community structure and strong dependence patterns among node pairs. This dependence can be modeled through mutual excitations, where an interaction event from a sender to a receiver node increases the possibility of future events among other node pairs. We provide statistical results for a class of models that we call dependent community Hawkes (DCH) models, which combine the stochastic block model with mutually exciting Hawkes processes for modeling both community structure and dependence among node pairs, respectively. We derive a non-asymptotic upper bound on the misclustering error of spectral clustering on the event count matrix as a function of the number of nodes and communities, time duration, and the amount of dependence in the model. Our result leverages recent results on bounding an appropriate distance between a multivariate Hawkes process count vector and a Gaussian vector, along with results from random matrix theory. We also propose a DCH model that incorporates only self and reciprocal excitation along with highly scalable parameter estimation using a Generalized Method of Moments (GMM) estimator that we demonstrate to be consistent for growing network size and time duration.

Problem

• Modeling community structure and dependence in temporal networks
• Analyzing misclustering error in spectral clustering for DCH models
• Developing scalable parameter estimation for dependent Hawkes processes

Innovation

• Combines stochastic block model with Hawkes processes
• Uses spectral clustering on event count matrix
• Scalable GMM estimator for parameter estimation