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arXiv · 2609.27278

Graph Learning with Spectral Connectivity Priors for Scarce Data

Mingxiao Liu·Bahar Oveisgharan·Bingyan Zou·Gene Cheung·H. Vicky Zhao·Feifei Gao
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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.

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Mingxiao Liu, Bahar Oveisgharan, Bingyan Zou, Gene Cheung, H. Vicky Zhao, Feifei Gao. 2026-09-23. Graph Learning with Spectral Connectivity Priors for Scarce Data. https://arxiv.org/abs/2609.27278

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