Learning the Exact Topology of Undirected Consensus Networks

TL;DR

This paper introduces a novel method using multivariate Wiener filtering and frequency response analysis to accurately reconstruct the exact topology of undirected consensus networks from time series data, even with correlated noise.

Contribution

It is the first approach to provably recover the true network structure of undirected consensus networks using Wiener filtering without prior knowledge of link weights.

Findings

Successfully reconstructs network topology in simulations

Effective in the presence of correlated noise

Validated on a real Raspberry Pi network

Abstract

In this article, we present a method to learn the interaction topology of a network of agents undergoing linear consensus updates in a non invasive manner. Our approach is based on multivariate Wiener filtering, which is known to recover spurious edges apart from the true edges in the topology. The main contribution of this work is to show that in the case of undirected consensus networks, all spurious links obtained using Wiener filtering can be identified using frequency response of the Wiener filters. Thus, the exact interaction topology of the agents is unveiled. The method presented requires time series measurements of the state of the agents and does not require any knowledge of link weights. To the best of our knowledge this is the first approach that provably reconstructs the structure of undirected consensus networks with correlated noise. We illustrate the effectiveness of the method developed through numerical simulations as well as experiments on a five node network of Raspberry Pis.