Product Graph Learning From Multi-Attribute Graph Signals with Inter-Layer Coupling

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 multiattribute data into matrices, and an exact solution via nearest Kro-necker 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.

1. INTRODUCTION

In recent years, there has been a growing trend in data science to develop tools for learning and making inference from signals or data observed on networks. The latter is also known as graph signals which form the subject of investigation in the emerging field of graph signal processing (GSP). Through modeling real-world networks as graphs and encoding the network data as filtered graph signals, an emerging trend is to develop tools for learning the latent graph topology from these network data; see [1], [2] and the references therein. These tools have widespread applications in the studies of social, financial, and biology networks [3].