Streaming Belief Propagation for Community Detection

TL;DR

This paper introduces a streaming belief propagation algorithm for community detection in dynamic networks, demonstrating its optimality over voting methods and validating results on synthetic and real data.

Contribution

It proposes a novel streaming belief propagation method for evolving networks, outperforming voting algorithms and achieving optimality in certain regimes.

Findings

Voting algorithms have fundamental limitations in streaming settings.

StreamBP achieves optimal detection performance in specific regimes.

Validated results on both synthetic and real-world network data.

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.