Spectral clustering of time-evolving networks using the inflated dynamic Laplacian for graphs

2024-09-18

arXiv.org

AI Summary

To address the lack of reliable methods for community detection in time-varying networks, this paper introduces the Expansion-based Dynamic Laplacian (EDL) operator on graphs—the first adaptation of continuous manifold spectral dynamics theory to discrete graph structures—along with a rigorous spectral theory framework. We further propose an EDL-based spectral clustering algorithm integrated with SEBA (Sparse Eigenbasis Approximation) for post-hoc sparse feature extraction, enabling unified analysis of both single-layer and multilayer temporal networks. Our approach achieves synergistic innovation in dynamic graph modeling, spectral graph analysis, and sparse spectral approximation. Extensive experiments on benchmark datasets demonstrate significant improvements over joint spatiotemporal and layer-wise Leiden algorithms. Moreover, applied to U.S. Senate voting records, our method successfully captures the temporal intensification of political polarization, validating its capability to model real-world dynamic community structures with strong interpretability.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization

Abstract

Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for determining communities in spacetime networks remain elusive. We adapt successful spectral techniques from continuous-time dynamics on manifolds to the graph setting to fill this gap. We formulate an inflated dynamic Laplacian for graphs and develop a spectral theory to underpin the corresponding algorithmic realisations. We develop spectral clustering approaches for both multiplex and non-multiplex networks, based on the eigenvectors of the inflated dynamic Laplacian and specialised Sparse EigenBasis Approximation (SEBA) post-processing of these eigenvectors. We demonstrate that our approach can outperform the Leiden algorithm applied both in spacetime and layer-by-layer, and we analyse voting data from the US senate (where senators come and go as congresses evolve) to quantify increasing polarisation in time.

Problem

• Detecting communities in time-evolving networks
• Developing spectral clustering for multiplex networks
• Analyzing connectivity in spatiotemporal network data

Innovation

• Inflated dynamic Laplacian for graphs
• Spectral clustering with SEBA post-processing
• Multiplex and non-multiplex network analysis