Nonparametric online monitoring of dynamic networks

Network sequence has been commonly used for describing the longitudinal pattern of a dynamic system. Proper online monitoring of a network sequence is thus important for detecting temporal structural changes of the system. To this end, there have been some discussions in the statistical process control (SPC) literature to first extract some features from the observed networks and then apply an SPC chart to monitor the extracted features sequentially over time. However, the features used in many existing methods are insensitive to some important network structural changes, and the control charts used cannot accommodate the complex structure of the extracted features properly. In this paper, we suggest using four specific features to describe the structure of an observed network, and their combination can reflect most network structural changes that we are interested in detecting in various applications. After the four features are extracted from the observed networks, we suggest using a multivariate nonparametric control chart to monitor the extracted features online. Numerical studies show that our proposed network monitoring method is more reliable and effective than some representative existing methods in various cases considered.