Clustering Time-Evolving Networks Using the Spatio-Temporal Graph Laplacian
This work addresses the challenge of clustering in time-varying graph structures, which is important for modeling complex dynamical systems, but it appears incremental as it extends existing spectral clustering methods to dynamic graphs.
The paper tackles the problem of identifying and analyzing communities in time-evolving graphs, such as social networks and traffic flow, by generalizing spectral clustering algorithms to dynamic graphs using canonical correlation analysis (CCA) and defining a spatio-temporal graph Laplacian, showing that it allows for clear interpretation of cluster structure evolution over time for directed and undirected graphs.
Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures is an important challenge. In this work, we generalize existing spectral clustering algorithms from static to dynamic graphs using canonical correlation analysis (CCA) to capture the temporal evolution of clusters. Based on this extended canonical correlation framework, we define the spatio-temporal graph Laplacian and investigate its spectral properties. We connect these concepts to dynamical systems theory via transfer operators, and illustrate the advantages of our method on benchmark graphs by comparison with existing methods. We show that the spatio-temporal graph Laplacian allows for a clear interpretation of cluster structure evolution over time for directed and undirected graphs.