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This paper introduces SCoGL, a novel framework that uses Laplacian spectral priors to enforce global connectivity in sparse graph learning from limited data. By optimizing an augmented graphical lasso objective, the method effectively recovers network structures and improves downstream tasks like signal denoising where observations are scarce. The approach bridges theoretical graph properties with practical machine learning applications for data-constrained environments.
Graph Learning with Spectral Connectivity Priors for Scarce Data
arXiv:2609.27278v1 Announce Type: new Abstract: 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 $\mathbf{W}$ 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 $\mathbf{W}$. Experiments show that the proposed SCoGL variants improve graph recovery and enhance downstream tasks such as graph signal denoising when signal observations are scarce.
Abstract: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 $\mathbf{W}$ 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 $\mathbf{W}$. Experiments show that the proposed SCoGL variants improve graph recovery and enhance downstream tasks such as graph signal denoising when signal observations are scarce.
5 pages, 1 figure. Submitted to IEEE ICASSP 2027
Machine Learning (cs.LG); Signal Processing (eess.SP)
arXiv:2609.27278 [cs.LG]
(or arXiv:2609.27278v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.27278 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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