Constrained Spectral Clustering for Dynamic Community Detection

TL;DR

This paper introduces a novel constrained spectral clustering method for dynamic community detection, modeling evolving communities with a new stochastic block model that accounts for different community evolution rates.

Contribution

It proposes a new stochastic block model for dynamic networks and derives a spectral clustering approach that incorporates community-specific evolution rates.

Findings

Effective on simulated dynamic networks

Performs well on real-world dynamic networks

Links statistical inference with spectral clustering

Abstract

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network science. Community detection aims to partition the network into sets of nodes that are densely connected internally but sparsely connected to other dense sets of nodes. Current work on community detection mostly focuses on static networks. However, many real world networks are dynamic, i.e. their structure and properties change with time, requiring methods for dynamic community detection. In this paper, we propose a new stochastic block model (SBM) for modeling the evolution of community membership. Unlike existing SBMs, the proposed model allows each community to evolve at a different rate. This new model is used to derive a maximum a posteriori estimator for community detection, which can be written as a constrained spectral clustering problem. In particular, the transition probabilities for each community modify the graph adjacency matrix at each time point. This formulation provides a relationship between statistical network inference and spectral clustering for dynamic networks. The proposed method is evaluated on both simulated and real dynamic networks.