Sequential Changepoint Approach for Online Community Detection

We present new algorithms for detecting the emergence of a community in large networks from sequential observations. The networks are modeled using Erdös-Renyi random graphs with edges forming between nodes in the community with higher probability. Based on statistical changepoint detection methodology, we develop three algorithms: the Exhaustive Search (ES), the Mixture, and the Hierarchical Mixture (H-Mix) methods. Performance of these methods is evaluated by the average run length (ARL), which captures the frequency of false alarms, and the detection delay. Numerical comparisons show that the ES method performs the best; however, it is exponentially complex. The Mixture method is polynomially complex by exploiting the fact that the size of the community is typically small in a large network. However, it may react to a group of active edges that do not form a community. This issue is resolved by the H-Mix method, which is based on a dendrogram decomposition of the network. We present an asymptotic analytical expression for ARL of the Mixture method when the threshold is large.