发表机构
Tsinghua University; York University（清华大学; 约克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对稀缺数据下的图学习问题，提出SCoGL框架，通过拉普拉斯谱先验促进全局连通性，结合投影梯度下降优化，实验证明能提升图恢复和下游任务性能。
AI 中文摘要
从稀缺数据中学习稀疏图在实际中很重要但具有挑战性。受扩展器类图所展现的局部稀疏性与强全局连通性的理想组合的启发，我们提出了谱连通性正则化图学习（SCoGL），这是一个将一族拉普拉斯谱先验纳入以显式促进全局连通性的框架。具体而言，SCoGL在目标邻接矩阵$\mathbf{W}$上增强了受组合拉普拉斯约束的图形套索（GLASSO）目标，并加入由拉普拉斯特征值计算得到的通用连通性先验。我们为几种代表性连通性先验推导了梯度，并开发了一种带Armijo回溯的投影梯度下降（PGD）算法来高效优化$\mathbf{W}$。实验表明，所提出的SCoGL变体在信号观测稀缺时改善了图恢复性能，并增强了图信号去噪等下游任务。
英文摘要
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.
Comments5 pages, 1 figure. Submitted to IEEE ICASSP 2027
