Streaming Belief Propagation for Community Detection

Abstract

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.

arXiv comment36 pages, 13 figures

References in corpus (10)

• Community structure in social and biological networks
• Community detection in graphs
• Finding community structure in very large networks
• Functional cartography of complex metabolic networks
• Defining and identifying communities in networks
• Community detection algorithms: a comparative analysis
• Stochastic blockmodels and community structure in networks
• Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
• Consistency of spectral clustering
• Finding One Community in a Sparse Graph