Graph Learning with Spectral Connectivity Priors for Scarce Data

2026-09-22

AI Summary

为了解决从稀缺数据中学习稀疏图的难题，本文提出了结合拉普拉斯谱先验促进全局连通性的SCoGL方法，并通过实验验证了其在图恢复和信号去噪任务上的有效性。

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.

Problem

• sparse graph
• scarce data
• global connectivity
• spectral priors
• graph learning

Innovation

• Spectral Connectivity-regularized Graph Learning (SCoGL)
• Laplacian Spectral Priors
• Projected Gradient Descent (PGD) with Armijo Backtracking
• Global Connectivity