Topology Identification of Dynamical Networks via Compressive Sensing

In this paper, we address the problem of topology identification of causal dynamical networks. Collecting the outputs of the nodes as time series, without any a priori knowledge about the structure of the network, we propose a data-driven algorithm that unveils the topology of the network and identifies the dynamics of connections. We cast the problem as a structured sparse signal recovery based on concepts borrowed from compressive sensing and matching pursuit. When sufficient data is available, the proposed algorithm results in perfect identification of general networks including feedback and self-loops. For noninvasive data, the proposed algorithm outperforms existing techniques. To demonstrate the effectiveness and advantages of the proposed method, we compare the simulation results with those of the Granger causality and other state-of-the-art techniques. As an empirical application, the proposed algorithm is deployed to construct a graphical network describing the interconnections of 30 companies in the Dow Jones stock market index with their prices ranging from January 2012 to June 2017.