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This paper considers learning a product graph from multi-attribute graphsignals. Our work is motivated by the widespread presence of multilayernetworks that feature interactions within and across graph layers. Focusing ona product graph setting with homogeneous layers, we propose a bivariatepolynomial graph filter model. We then consider the topology inference problemsthru adapting existing spectral methods. We propose two solutions for therequired spectral estimation step: a simplified solution via unfolding themulti-attribute data into matrices, and an exact solution via nearest Kroneckerproduct decomposition (NKD). Interestingly, we show that strong inter-layercoupling can degrade the performance of the unfolding solution while the NKDsolution is robust to inter-layer coupling effects. Numerical experiments showefficacy of our methods.

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