Graph reconstruction from the observation of diffused signals

TL;DR

This paper proposes a method to reconstruct the underlying graph structure from diffused signals, assuming they originate from initially independent signals, and demonstrates its effectiveness through experiments.

Contribution

It introduces a novel approach for inferring graph structures solely from diffused signals, without prior knowledge of the graph, under diffusion assumptions.

Findings

Successfully reconstructs known graphs from diffused signals

Achieves high accuracy in graph recovery in experimental validation

Applicable to sensor networks with unknown support structures

Abstract

Signal processing on graphs has received a lot of attention in the recent years. A lot of techniques have arised, inspired by classical signal processing ones, to allow studying signals on any kind of graph. A common aspect of these technique is that they require a graph correctly modeling the studied support to explain the signals that are observed on it. However, in many cases, such a graph is unavailable or has no real physical existence. An example of this latter case is a set of sensors randomly thrown in a field which obviously observe related information. To study such signals, there is no intuitive choice for a support graph. In this document, we address the problem of inferring a graph structure from the observation of signals, under the assumption that they were issued of the diffusion of initially i.i.d. signals. To validate our approach, we design an experimental protocol, in which we diffuse signals on a known graph. Then, we forget the graph, and show that we are able to retrieve it very precisely from the only knowledge of the diffused signals.