Graph Learning with Spectral Connectivity Priors for Scarce Data
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Computer Science > Machine Learning
Title:Graph Learning with Spectral Connectivity Priors for Scarce Data
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.
| Comments: | 5 pages, 1 figure. Submitted to IEEE ICASSP 2027 |
| Subjects: | Machine Learning (cs.LG); Signal Processing (eess.SP) |
| Cite as: | arXiv:2609.27278 [cs.LG] |
| (or arXiv:2609.27278v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.27278
arXiv-issued DOI via DataCite (pending registration)
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