Optimality of Graph Scanning Statistic for Online Community Detection

TL;DR

This paper analyzes the optimality of a graph scan statistic for online community detection in streaming network data, focusing on local changes in subgraphs within an Erdos-Renyi model, and provides theoretical and empirical validation.

Contribution

It establishes the asymptotic optimality of a GLR-based scan statistic for detecting local subgraph changes in streaming graphs.

Findings

The proposed detection method is asymptotically optimal.

Simulation results demonstrate the efficiency of the algorithm.

The approach effectively identifies change-points in streaming network data.

Abstract

Sequential change-point detection for graphs is a fundamental problem for streaming network data types and has wide applications in social networks and power systems. Given fixed vertices and a sequence of random graphs, the objective is to detect the change-point where the underlying distribution of the random graph changes. In particular, we focus on the local change that only affects a subgraph. We adopt the classical Erdos-Renyi model and revisit the generalized likelihood ratio (GLR) detection procedure. The scan statistic is computed by sequentially estimating the most-likely subgraph where the change happens. We provide theoretical analysis for the asymptotic optimality of the proposed procedure based on the GLR framework. We demonstrate the efficiency of our detection algorithm using simulations.