# Learning product graphs from multidomain signals

arXiv: https://arxiv.org/abs/1911.07411 · HTML: https://mlsanity.com/paper/1911.07411/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Learning Product Graphs from Spectral Templates](https://mlsanity.com/paper/2211.02893/) (2022)
- [ProductGraphSleepNet: Sleep Staging using Product Spatio-Temporal Graph Learning with Attentive Temporal Aggregation](https://mlsanity.com/paper/2212.04881/) (2022)
- [Learning Cartesian Product Graphs with Laplacian Constraints](https://mlsanity.com/paper/2402.08105/) (2024)
- [Learning Kronecker-Structured Graphs from Smooth Signals](https://mlsanity.com/paper/2505.09822/) (2025)
- [Role-Specific Predictive Geometries for Nonstationary Multivariate Graph-Signal Forecasting](https://mlsanity.com/paper/2609.06519/) (2026)

## Abstract (arXiv)

In this paper, we focus on learning the underlying product graph structure from multidomain training data. We assume that the product graph is formed from a Cartesian graph product of two smaller factor graphs. We then pose the product graph learning problem as the factor graph Laplacian matrix estimation problem. To estimate the factor graph Laplacian matrices, we assume that the data is smooth with respect to the underlying product graph. When the training data is noise free or complete, learning factor graphs can be formulated as a convex optimization problem, which has an explicit solution based on the water-filling algorithm. The developed framework is illustrated using numerical experiments on synthetic data as well as real data related to air quality monitoring in India.