Blind Graph Matching Using Graph Signals

TL;DR

This paper introduces a novel method for blind graph matching that directly uses observed graph signals and their covariance matrices, avoiding the need to infer unknown graph topologies, and demonstrates its effectiveness through theoretical analysis and numerical experiments.

Contribution

It proposes a new blind graph matching approach based on sample covariance matrices of graph signals, bypassing topology inference and improving accuracy.

Findings

Convergence to known topology results with large sample sizes

Performance surpasses methods relying on estimated graph topologies

Effective in scenarios with unknown underlying graphs

Abstract

Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological network functions across species. However, when the underlying graphs are unknown, the use of conventional graph matching methods requires inferring the graph topologies first, a process that is highly sensitive to observation errors. In this paper, we tackle the blind graph matching problem with unknown underlying graphs directly using observations of graph signals, which are generated from graph filters applied to graph signal excitations. We propose to construct sample covariance matrices from the observed signals and match the nodes based on the selected sample eigenvectors. Our analysis shows that the blind matching outcome converges to the result obtained with known graph topologies when the signal sampling size is large and the signal noise is small. Numerical results showcase the performance improvement of the proposed algorithm compared to matching two estimated underlying graphs learned from the graph signals.