# Accelerated Graph Learning from Smooth Signals

arXiv: https://arxiv.org/abs/2110.09677 · HTML: https://mlsanity.com/paper/2110.09677/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (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 Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information](https://mlsanity.com/paper/2007.03653/) (2020)
- [Learning Graphs with Monotone Topology Properties and Multiple Connected Components](https://mlsanity.com/paper/1705.10934/) (2017)
- [Graph topology inference based on sparsifying transform learning](https://mlsanity.com/paper/1806.01701/) (2018)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)
- [Network Topology Identification from Spectral Templates](https://mlsanity.com/paper/1604.02610/) (2016)

## Built on by (most cited first, 16 of 16)

- [Non-negative Weighted DAG Structure Learning](https://mlsanity.com/paper/2409.07880/) (2024)
- [Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals](https://mlsanity.com/paper/2202.02815/) (2022)
- [Graph Structure Learning with Interpretable Bayesian Neural Networks](https://mlsanity.com/paper/2406.14786/) (2024)
- [Joint graph learning from Gaussian observations in the presence of hidden nodes](https://mlsanity.com/paper/2212.01816/) (2022)
- [Graph Laplacian Learning with Exponential Family Noise](https://mlsanity.com/paper/2306.08201/) (2023)
- [A Unified Framework for Fair Spectral Clustering With Effective Graph Learning](https://mlsanity.com/paper/2311.13766/) (2023)
- [Learning to Identify Graphs from Node Trajectories in Multi-Robot Networks](https://mlsanity.com/paper/2307.04374/) (2023)
- [Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals](https://mlsanity.com/paper/2310.19005/) (2023)
- [Online Proximal ADMM for Graph Learning from Streaming Smooth Signals](https://mlsanity.com/paper/2409.12916/) (2024)
- [Signature-Kernel One-Class Learning with Manifold Regularisation for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2507.23449/) (2025)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [Non-negative DAG Learning from Time-Series Data](https://mlsanity.com/paper/2512.07267/) (2025)
- [Topology Identification and Inference over Graphs](https://mlsanity.com/paper/2512.10183/) (2025)
- [Dynamic Elliptical Graph Factor Models via Riemannian Optimization with Geodesic Temporal Regularization](https://mlsanity.com/paper/2605.18316/) (2026)
- [Directed Graph Topology Inference via Graph Filter Identification](https://mlsanity.com/paper/2606.27455/) (2026)
- [Multi-Source Wasserstein Distributionally Robust Graph Learning](https://mlsanity.com/paper/2608.19914/) (2026)

## Abstract (arXiv)

We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network inverse problem known to yield high-quality graph solutions. Unlike existing solvers, the novel iterations come with global convergence rate guarantees and do not require additional step-size tuning. Reproducible simulated tests demonstrate the effectiveness of the proposed method in accurately recovering random and real-world graphs, markedly faster than state-of-the-art alternatives and without incurring an extra computational burden.