Modeling and monitoring unweighted networks with directed interactions

Abstract

Networks have been widely employed to represent interactive relationships among individual units in complex systems such as the Internet of Things. Assignable causes in systems can lead to abrupt increased or decreased frequency of communications within the corresponding network, which allows us to detect such assignable causes by monitoring the communication level of the network. However, existing statistical process control methods for unweighted networks have scarcely incorporated either the network sparsity or the direction of interactions between two network nodes, i.e., dyadic interaction. Regarding this, we establish a matrix-form model to characterize directional dyadic interactions in time-independent unweighted networks. With inactive dyadic interactions excluded, the proposed procedure of parameter estimation achieves higher consistency with less computational cost than its alternative when networks are large-scale and sparse. Using the generalized likelihood ratio test, the work derives two schemes for monitoring directed unweighted networks. The first can be used in general cases whereas the second incorporates a priori shift information to improve change detection efficiency in some cases and estimate the location of a single shifted parameter. Simulation study and a real application are provided to demonstrate the advantages and effectiveness of proposed schemes.