Topology Identification of Directed Dynamical Networks via Power Spectral Analysis

TL;DR

This paper introduces spectral analysis-based algorithms to identify the topology of directed and undirected linear time-invariant networks from their response to stationary noise inputs, including methods for structure and weight recovery.

Contribution

It presents new algorithms for reconstructing network topology and weights using power spectral densities, applicable to various network types and with reduced computational costs.

Findings

Successfully reconstructs Boolean network structure from responses.

Recovers exact network weights and noise spectral densities with known eigenpairs.

Provides specialized algorithms for nonreciprocal and undirected networks.

Abstract

We address the problem of identifying the topology of an unknown weighted, directed network of LTI systems stimulated by wide-sense stationary noises of unknown power spectral densities. We propose several reconstruction algorithms based on the cross-power spectral densities of the network's response to the input noises. Our first algorithm reconstructs the Boolean structure (i.e., existence and directions of links) of a directed network from a series of dynamical responses. Moreover, we propose a second algorithm to recover the exact structure of the network (including edge weights), as well as the power spectral density of the input noises, when an eigenvalue-eigenvector pair of the connectivity matrix is known (for example, Laplacian connectivity matrices). Finally, for the particular cases of nonreciprocal networks (i.e., networks with no directed edges pointing in opposite directions) and undirected networks, we propose specialized algorithms that result in a lower computational cost.