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.

Source: arXiv cs.LG | 2026-09-24