# Graph Learning with Spectral Connectivity Priors for Scarce Data

arXiv: https://arxiv.org/abs/2609.27278 · HTML: https://mlsanity.com/paper/2609.27278/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 23 Sep 2026.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Learning heat diffusion graphs](https://mlsanity.com/paper/1611.01456/) (2016)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Feature Graph Learning for 3D Point Cloud Denoising](https://mlsanity.com/paper/1907.09138/) (2019)
- [Signed Graph Metric Learning via Gershgorin Disc Perfect Alignment](https://mlsanity.com/paper/2006.08816/) (2020)
- [Efficient Graph Laplacian Estimation by Proximal Newton](https://mlsanity.com/paper/2302.06434/) (2023)
- [Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming](https://mlsanity.com/paper/2409.07794/) (2024)
- [Learning Cartesian Product Graphs with Laplacian Constraints](https://mlsanity.com/paper/2402.08105/) (2024)
- [A Connectedness Constraint for Learning Sparse Graphs](https://mlsanity.com/paper/1708.09021/) (2017)
- [Sparse Graph Learning from Sparse Data via Fiedler Number Maximization](https://mlsanity.com/paper/2604.26132/) (2026)

## Abstract (arXiv)

Learning a sparse graph from scarce data is practically important but challenging. Motivated by the desirable combination of local sparsity and strong global connectivity exhibited by expander-like graphs, we propose spectral connectivity-regularized graph learning (SCoGL), a framework that incorporates a family of Laplacian spectral priors to explicitly promote global connectivity. Specifically, SCoGL augments a combinatorial-Laplacian-constrained graphical lasso (GLASSO) objective over a target adjacency matrix W with a general connectivity prior computed from Laplacian eigenvalues. We derive gradients for several representative connectivity priors and develop a projected gradient descent (PGD) algorithm with Armijo backtracking to efficiently optimize W. Experiments show that the proposed SCoGL variants improve graph recovery and enhance downstream tasks such as graph signal denoising when signal observations are scarce.