Fréchet-Statistics-Based Change Point Detection in Dynamic Social Networks

Rui Luo, Vikram Krishnamurthy

Abstract: This article proposes a method to detect change points in dynamic social networks using Fréchet statistics. We address two main questions: 1) what metric can quantify the distances between graph Laplacians in a dynamic network and enable efficient computation, and 2) how can the Fréchet statistics be extended to detect multiple change points while maintaining the significance level of the hypothesis test? Our solution defines a metric space for graph Laplacians using the log-Euclidean metric, enabling a closed-form formula for Fréchet mean and variance. We present a framework for change point detection using Fréchet statistics and extend it to multiple change points with binary segmentation. The proposed algorithm uses incremental computation for Fréchet mean and variance to improve efficiency and is validated on simulated and four real-world datasets, namely, the UCI message dataset, the SFHH interaction dataset, the stack overflow Q&A dataset, and the Enron email dataset.