# Learning graphs from data: A signal representation perspective

arXiv: https://arxiv.org/abs/1806.00848 · HTML: https://mlsanity.com/paper/1806.00848/

## Key facts

- Cited by 119 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2018.

## Built on by (most cited first, 30 of 119)

- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognition](https://mlsanity.com/paper/2112.03328/) (2021)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networks](https://mlsanity.com/paper/2201.12741/) (2022)
- [Benchmarking Positional Encodings for GNNs and Graph Transformers](https://mlsanity.com/paper/2411.12732/) (2024)
- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering](https://mlsanity.com/paper/2206.02386/) (2022)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [Graph Concept Bottleneck Models](https://mlsanity.com/paper/2508.14255/) (2025)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)
- [Temporal Graph Signal Decomposition](https://mlsanity.com/paper/2106.13517/) (2021)
- [Learning to Infer Structures of Network Games](https://mlsanity.com/paper/2206.08119/) (2022)
- [Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals](https://mlsanity.com/paper/2404.02621/) (2024)
- [Interpretable Lightweight Transformer via Unrolling of Learned Graph Smoothness Priors](https://mlsanity.com/paper/2406.04090/) (2024)
- [Beyond the Federation: Topology-aware Federated Learning for Generalization to Unseen Clients](https://mlsanity.com/paper/2407.04949/) (2024)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [HGAttack: Transferable Heterogeneous Graph Adversarial Attack](https://mlsanity.com/paper/2401.09945/) (2024)
- [SGL: Spectral Graph Learning from Measurements](https://mlsanity.com/paper/2104.07867/) (2021)
- [Sparse Graph Learning Under Laplacian-Related Constraints](https://mlsanity.com/paper/2111.08161/) (2021)
- [Learning Graph Structure from Convolutional Mixtures](https://mlsanity.com/paper/2205.09575/) (2022)
- [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)
- [How Does Message Passing Improve Collaborative Filtering?](https://mlsanity.com/paper/2404.08660/) (2024)
- [Distributionally Robust Graph Learning from Smooth Signals under Moment Uncertainty](https://mlsanity.com/paper/2105.05458/) (2021)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Community-based anomaly detection using spectral graph filtering](https://mlsanity.com/paper/2201.09936/) (2022)
- [Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals](https://mlsanity.com/paper/2202.02815/) (2022)

## Abstract (arXiv)

The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets, it is thus desirable to infer or learn a graph topology from the data. In this tutorial overview, we survey solutions to the problem of graph learning, including classical viewpoints from statistics and physics, and more recent approaches that adopt a graph signal processing (GSP) perspective. We further emphasize the conceptual similarities and differences between classical and GSP-based graph inference methods, and highlight the potential advantage of the latter in a number of theoretical and practical scenarios. We conclude with several open issues and challenges that are keys to the design of future signal processing and machine learning algorithms for learning graphs from data.