# Learning Product Graphs from Spectral Templates

arXiv: https://arxiv.org/abs/2211.02893 · HTML: https://mlsanity.com/paper/2211.02893/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 63 references that are in the map.
- First posted on arXiv 5 Nov 2022.

## Builds on (most cited first, 25 of 25)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [DeepSleepNet: a Model for Automatic Sleep Stage Scoring based on Raw Single-Channel EEG](https://mlsanity.com/paper/1703.04046/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [A deep learning architecture for temporal sleep stage classification using multivariate and multimodal time series](https://mlsanity.com/paper/1707.03321/) (2017)
- [Multi-View Spatial-Temporal Graph Convolutional Networks with Domain Generalization for Sleep Stage Classification](https://mlsanity.com/paper/2109.01824/) (2021)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Vertex-Frequency Analysis on Graphs](https://mlsanity.com/paper/1307.5708/) (2013)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [A Time-Vertex Signal Processing Framework](https://mlsanity.com/paper/1705.02307/) (2017)
- [Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information](https://mlsanity.com/paper/2007.03653/) (2020)
- [Joint Inference of Multiple Graphs from Matrix Polynomials](https://mlsanity.com/paper/2010.08120/) (2020)
- [Covariance Estimation in High Dimensions via Kronecker Product Expansions](https://mlsanity.com/paper/1302.2686/) (2013)
- [Novel Multidimensional Models of Opinion Dynamics in Social Networks](https://mlsanity.com/paper/1505.04920/) (2015)
- [Product Graph Learning from Multi-domain Data with Sparsity and Rank Constraints](https://mlsanity.com/paper/2012.08090/) (2020)
- [Learning Product Graphs Underlying Smooth Graph Signals](https://mlsanity.com/paper/2002.11277/) (2020)
- [Estimating Network Processes via Blind Identification of Multiple Graph Filters](https://mlsanity.com/paper/1909.12980/) (2019)
- [Learning product graphs from multidomain signals](https://mlsanity.com/paper/1911.07411/) (2019)
- [Forecasting Multi-Dimensional Processes over Graphs](https://mlsanity.com/paper/2004.08260/) (2020)
- [One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations](https://mlsanity.com/paper/1304.5038/) (2013)
- [UNLocBoX: A MATLAB convex optimization toolbox for proximal-splitting methods](https://mlsanity.com/paper/1402.0779/) (2014)

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

- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [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)
- [Second-Order Tensorial Partial Differential Equations on Graphs](https://mlsanity.com/paper/2509.02015/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can provide practical constraints in the GL approach. One applicable constraint can infer a graph with desired frequency signatures, i.e., spectral templates. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional graph signals. To address this issue and in the case of the underlying graph having graph product structure, we propose learning product (high dimensional) graphs from product spectral templates with significantly reduced complexity rather than learning them directly from high-dimensional graph signals, which, to the best of our knowledge, has not been addressed in the related areas. In contrast to the rare current approaches, our approach can learn all types of product graphs (with more than two graphs) without knowing the type of graph products and has fewer parameters. Experimental results on both the synthetic and real-world data, i.e., brain signal analysis and multi-view object images, illustrate explainable and meaningful factor graphs supported by expert-related research, as well as outperforming the rare current restricted approaches.