  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.
