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

arXiv: https://arxiv.org/abs/2211.00909 · HTML: https://mlsanity.com/paper/2211.00909/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [LogSpecT: Feasible Graph Learning Model from Stationary Signals with Recovery Guarantees](https://mlsanity.com/paper/2305.01379/) (2023)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

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.