Topology identification under spatially correlated noise

This article addresses the problem of reconstructing the topology of a network of agents interacting via linear dynamics, while being excited by exogenous stochastic sources that are possibly correlated across the agents, from time-series measurements alone. It is shown, under the assumption that the correlations are affine in nature, such network of nodal interactions is equivalent to a network with added agents. The added agents are represented by nodes that are latent, where no corresponding time-series measurements are available; however, here all the exogenous excitements are spatially (that is, across agents) uncorrelated. Generalizing affine correlations, it is shown that, under polynomial correlations, the latent nodes in the expanded networks can be excited by clusters of noise sources, where the clusters are uncorrelated with each other. The clusters can be replaced with a single noise source if the latent nodes are allowed to have non-linear interactions. Finally, using the sparse plus low-rank matrix decomposition of the imaginary part of the inverse power spectral density matrix (IPSDM) of the time-series data, the topology of the network is reconstructed. Under non conservative assumptions, the correlation graph of the noise sources is retrieved. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

This article addresses the problem of reconstructing the topology of a network of agents with linear dynamics and exogenous stochastic sources from time-series measurements alone. It shows that under affine correlations, the network can be represented as a network with added latent agents. The topology is reconstructed using the sparse plus low-rank matrix decomposition method.