# Structured Graph Learning Via Laplacian Spectral Constraints

arXiv: https://arxiv.org/abs/1909.11594 · HTML: https://mlsanity.com/paper/1909.11594/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2019.

## Built on by (most cited first, 20 of 20)

- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [A Unified Framework for Optimization-Based Graph Coarsening](https://mlsanity.com/paper/2210.00437/) (2022)
- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)
- [Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decomposition](https://mlsanity.com/paper/2309.13405/) (2023)
- [Efficient Graph Laplacian Estimation by Proximal Newton](https://mlsanity.com/paper/2302.06434/) (2023)
- [Joint graph learning from Gaussian observations in the presence of hidden nodes](https://mlsanity.com/paper/2212.01816/) (2022)
- [Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes](https://mlsanity.com/paper/2503.08760/) (2025)
- [SF-SGL: Solver-Free Spectral Graph Learning from Linear Measurements](https://mlsanity.com/paper/2302.04384/) (2023)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [Learning Multi-Attribute Differential Graphs with Non-Convex Penalties](https://mlsanity.com/paper/2505.09748/) (2025)
- [Sparse Graph Learning from Sparse Data via Fiedler Number Maximization](https://mlsanity.com/paper/2604.26132/) (2026)
- [Clustering Alzheimer's Disease Subtypes via Similarity Learning and Graph Diffusion](https://mlsanity.com/paper/2410.03937/) (2024)
- [Adversarial-Robustness-Guided Graph Pruning](https://mlsanity.com/paper/2411.12331/) (2024)
- [Learning Networks from Wide-Sense Stationary Stochastic Processes](https://mlsanity.com/paper/2412.03768/) (2024)
- [Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming](https://mlsanity.com/paper/2506.01826/) (2025)
- [Including Node Textual Metadata in Laplacian-constrained Gaussian Graphical Models](https://mlsanity.com/paper/2602.15920/) (2026)
- [Robust Learning on Heterogeneous Graphs with Heterophily: A Graph Structure Learning Approach](https://mlsanity.com/paper/2604.27387/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible to convert the structural constraints of structure into eigenvalue constraints of the graph Laplacian matrix. Then we introduce a unified graph learning framework, lying at the integration of the spectral properties of the Laplacian matrix with Gaussian graphical modeling that is capable of learning structures of a large class of graph families. The proposed algorithms are provably convergent and practically amenable for large-scale semi-supervised and unsupervised graph-based learning tasks. Extensive numerical experiments with both synthetic and real data sets demonstrate the effectiveness of the proposed methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.