A Spectral Framework for Tracking Communities in Evolving Networks

TL;DR

This paper introduces a spectral framework for tracking communities in evolving networks by modeling the problem as subspace tracking on the Grassmann manifold, enabling improved dynamic community detection across diverse network types.

Contribution

It generalizes static spectral community detection methods to dynamic settings using Riemannian optimization, enhancing performance on various complex temporal networks.

Findings

Achieves improved community detection in synthetic and real networks

Handles diverse network types including weighted, signed, and bipartite

Provides a unified framework for multiple spectral methods

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 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.