CP-Squared: A method for change point detection in core–periphery networks

Abstract

Time series of networks are increasingly prevalent in modern data and pose unique challenges to pattern extraction and change detection. In this paper we develop and present a novel methodology to detect regime changes within a sequence of networks that have overlapping and evolving community structure. The core of the methodology is a non-negative matrix factorization that maximizes a Poisson likelihood subject to a penalty that accounts for sparsity in the network. By fitting the factorization model over a rolling window with a fast numerical optimization algorithm, change detection is accomplished by statistical monitoring of the matrix factors’ evolution. A novel statistic is used to characterize the overall network evolution as well as the contribution of each node to the change. We demonstrate that the proposed methodology compares favorably with alternative techniques for on-the-go network change detection using synthetic and real data. A detailed case study on the 2007–2009 financial crisis and the European sovereign debt crisis shows the promise of the methodology for regulators as it identifies particular banks that contributed to each crisis in addition to identifying changing market conditions.