Streaming Belief Propagation for Community Detection
This addresses the challenge of efficiently detecting communities in real-world streaming networks, offering a novel solution with proven theoretical guarantees.
The paper tackles the problem of community detection in dynamic networks where nodes join over time, proving that standard voting algorithms have fundamental limitations and introducing a streaming belief-propagation approach that achieves optimality in certain regimes.
The community detection problem requires to cluster the nodes of a network into a small number of well-connected "communities". There has been substantial recent progress in characterizing the fundamental statistical limits of community detection under simple stochastic block models. However, in real-world applications, the network structure is typically dynamic, with nodes that join over time. In this setting, we would like a detection algorithm to perform only a limited number of updates at each node arrival. While standard voting approaches satisfy this constraint, it is unclear whether they exploit the network information optimally. We introduce a simple model for networks growing over time which we refer to as streaming stochastic block model (StSBM). Within this model, we prove that voting algorithms have fundamental limitations. We also develop a streaming belief-propagation (StreamBP) approach, for which we prove optimality in certain regimes. We validate our theoretical findings on synthetic and real data.