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.

摘要

网络已被广泛用于表示复杂系统（例如物联网）中各个单元之间的交互关系。系统中的可分配原因可能导致相应网络内通信的频率突然增加或减少，这使我们可以通过监视网络的通信级别来检测此类可分配原因。但是，现有的用于非加权网络的统计过程控制方法几乎没有合并网络稀疏性或两个网络节点之间的交互作用（即二元交互作用）的方向。对此，我们建立了一个矩阵形式的模型来表征与时间无关的非加权网络中的定向二元相互作用。排除无效的二元互动，当网络规模大且稀疏时，所提出的参数估计过程比其替代方法具有更高的一致性，且计算成本更低。使用广义似然比检验，这项工作得出了两种用于监视有向非加权网络的方案。第一个可以在一般情况下使用，而第二个可以合并先验移位信息以在某些情况下提高变化检测效率并估计单个移位参数的位置。仿真研究和实际应用证明了所提方案的优势和有效性。