Multi-scale anomaly detection in complex dynamic networks

Graphs arise naturally in a wide range of disciplines and applications since they capture the association between entities of a complex network. Recently, there has been an interest in time-evolving or dynamic graphs which can capture the change in the relational information across time. One important problem of interest in dynamic graphs is to detect the changes or anomalies in graph structure across time and identify the edges that conribute to these anomalies. In this paper, we propose a multi-scale analysis of dynamic graphs based on the Wavelet Packet Decomposition to separate the transient edge activity from the stationary background activity. Modeling the wavelet packet coefficients using a Gaussian Mixture Model, we derive a Neyman Pearson detector to identify anomalous edges both in time and space. Experiments illustrate the effectiveness of the method for both simulated and real dynamic networks.