Networks are thought to be the representation of complex systems that comprise of a number of components that act and interact with each other to mediate system behavior. A common practice to construct the network from data is to directly take dyadic or pairwise connections (edges) among components (nodes), but many complex systems can be better characterized by higher-order networks (HONs) where interactions may occur between more than two nodes. In this talk, I will present a matrix algorithm for reconstructing high-order connectivity networks from general data domains. The model has three characteristics. First, it captures a full set of network properties by estimating bidirectional, signed, and weighted high-order interactions. Second, the model coalesces static data into its quasi-dynamic representation, allowing for the dynamic change of HONs across different contexts. Third, through the implementation of high-dimensional statistical models, the model can reconstruct multilayer, multiscale, multiplex, and multispace HONs from any dimension of big data. High-order dynamical interactome networks inferred from our model provide a tool to understand the fundamental structures that control and modulate the behavior of complex systems.
