Topology Learning of Radial Dynamical Systems with Latent Nodes
For researchers in network topology inference, this provides a method to handle latent nodes in radial dynamical systems, though the radial assumption limits its generality.
This paper proposes a method to reconstruct the topology of partially observed radial networks of linear dynamical systems, recovering edges up to four hops away and identifying unobserved nodes using only time-series data from observed nodes. The algorithm is demonstrated on an electric grid distribution system.
In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density matrix and recovers edges involving nodes up to four hops away in the underlying topology. We then present an algorithm with provable guarantees, which eliminates the spurious links obtained and also identifies the location of the unobserved nodes in the inferred topology. The algorithm recovers the exact topology of the network by using only time-series of the states at the observed nodes. The effectiveness of the method developed is demonstrated by applying it on a typical distribution system of the electric grid.