A multi-scale energy detector for anomaly detection in dynamic networks

Complex networks have attracted a lot of attention for representing relational data, where the weights of the edges, where edges´ weights show the strength of relationships. Complex networks have found numerous applications in social and biological sciences. Studying the topology of these networks is important for a better understanding of the underlying systems and data. Currently, most of the network analysis tools are limited to static networks. However, most networks of interest have edges or relationships that vary across time. Therefore, there is a need to develop methods for the study of these dynamic networks. In this paper, we introduce another aspect of threat detection, which is identifying abrupt changes in edges´ weights over time. Wavelet decomposition method is used to separate the transient activity from the stationary activity in the edges. A hypothesis testing is proposed for the wavelet coefficients to detect any anomalous edges. Finally, the time points where the anomalous activity occurs are identified through the ratio of the energy of the anomalous to normal edges.