Spectral identification of networks with generalized diffusive coupling

TL;DR

This paper extends spectral network identification to vector-valued diffusive couplings, providing theoretical insights and a numerical method based on dynamic mode decomposition to infer network eigenvalues from local measurements.

Contribution

It introduces a generalized framework for spectral network identification with vector-valued coupling and proposes a novel numerical approach leveraging dynamic mode decomposition.

Findings

Theoretical properties of the generalized eigenvalue problem are established.

A numerical method based on dynamic mode decomposition is developed.

The approach enables inference of network eigenvalues from limited local data.

Abstract

Spectral network identification aims at inferring the eigenvalues of the Laplacian matrix of a network from measurement data. This allows to capture global information on the network structure from local measurements at a few number of nodes. In this paper, we consider the spectral network identification problem in the generalized setting of a vector-valued diffusive coupling. The feasibility of this problem is investigated and theoretical results on the properties of the associated generalized eigenvalue problem are obtained. Finally, we propose a numerical method to solve the generalized network identification problem, which relies on dynamic mode decomposition and leverages the above theoretical results.