A Spectral Framework for Tracking Communities in Evolving Networks
This work addresses the challenge of dynamic community detection for applications in fields like neuroscience and sociology, representing an incremental advancement by extending existing spectral methods to temporal settings.
The authors tackled the problem of tracking communities in evolving networks by generalizing static spectral clustering methods into a subspace tracking framework on the Grassmann manifold, achieving greatly improved dynamic community detection results across various network types.
Discovering and tracking communities in time-varying networks is an important task in network science, motivated by applications in fields ranging from neuroscience to sociology. In this work, we characterize the celebrated family of spectral methods for static clustering in terms of the low-rank approximation of high-dimensional node embeddings. From this perspective, it becomes natural to view the evolving community detection problem as one of subspace tracking on the Grassmann manifold. While the resulting optimization problem is nonconvex, we adopt a block majorize-minimize Riemannian optimization scheme to learn the Grassmann geodesic which best fits the data. Our framework generalizes any static spectral community detection approach and leads to algorithms achieving favorable performance on synthetic and real temporal networks, including those that are weighted, signed, directed, mixed-membership, multiview, hierarchical, cocommunity-structured, bipartite, or some combination thereof. We demonstrate how to specifically cast a wide variety of methods into our framework, and demonstrate greatly improved dynamic community detection results in all cases.