A Spectral Framework for Tracking Communities in Evolving Networks

Jacob Hume, Laura Balzano

Keywords: spectral partitioning, dynamic networks, community detection, Grassmann geometry, Riemannian optimization, graph embedding, nonlinear dimensionality reduction

TL;DR: We provide a framework for turning any spectral community detection method into a high-performing dynamic community tracking method that leverages Grassmannian curve fitting to low-rank approximations of clustering matrices.

Abstract: 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 recently proposed 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.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Software: https://github.com/JacobH140/spectral-dcd, https://github.com/JacobH140/century-of-college-football

Submission Number: 137