Topology Learning of Linear Dynamical Systems With Latent Nodes Using Matrix Decomposition

In this article, we present a novel approach to reconstruct the topology of networked linear dynamical systems with latent nodes. The network is allowed have directed loops and bi-directed edges. main relies on unique decomposition inverse power spectral density matrix (IPSDM) obtained from observed nodes as sum sparse low-rank matrices. We provide conditions methods for decomposing IPSDM into components. component yields moral graph (MG) associated nodes, retrieves parents, children spouses (the Markov Blanket) hidden article provides necessary sufficient given skew symmetric For large class systems, imaginary part matrix, components identify MG well Blanket all spurious links in formed by can be identified. Assuming required identifiability, between reconstructed, thus retrieving exact IPSDM. Moreover, finite data, bounds entry-wise distance true estimated IPSDMs.