Product Graph Learning from Multi-attribute Graph Signals with Inter-layer Coupling

TL;DR

This paper introduces methods for learning product graphs from multi-attribute signals in multilayer networks, proposing spectral estimation techniques that handle inter-layer coupling effects effectively.

Contribution

It develops a bivariate polynomial graph filter model and two spectral estimation solutions, including a robust NKD approach for topology inference in multilayer graphs.

Findings

NKD method is robust to inter-layer coupling.

Unfolding solution performance degrades with strong coupling.

Numerical experiments validate the proposed methods.

Abstract

This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph setting with homogeneous layers, we propose a bivariate polynomial graph filter model. We then consider the topology inference problems thru adapting existing spectral methods. We propose two solutions for the required spectral estimation step: a simplified solution via unfolding the multi-attribute data into matrices, and an exact solution via nearest Kronecker product decomposition (NKD). Interestingly, we show that strong inter-layer coupling can degrade the performance of the unfolding solution while the NKD solution is robust to inter-layer coupling effects. Numerical experiments show efficacy of our methods.