发表机构
Lund University; Linköping University（隆德大学; 林雪平大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对样本数少于节点数的欠定图估计问题，提出一种基于有效电阻正则化的非迭代图拉普拉斯估计器，配合简单稀疏化，在牺牲部分边和权重恢复精度的代价下大幅降低中等规模图的计算成本。
AI 中文摘要
从含噪声的节点观测中推断网络拓扑是图信号处理中的一个核心问题。本文考虑高斯马尔可夫随机场中受拉普拉斯约束的图估计，重点关注样本数小于图节点数的欠定情形。现有方法通常将该问题表述为稀疏正则化的最大似然估计问题。虽然这些方法有效，但通常需要迭代优化，且在拉普拉斯约束下计算负担较重。相反，我们提出了一种使用有效电阻进行正则化的非迭代图拉普拉斯估计器，并通过简单的稀疏化过程对该方法进行评估。实验表明，在所考虑的数据集上，尽管在边和权重恢复方面存在一定的权衡，但中等规模图的计算成本可大幅降低。
英文摘要
Inferring network topology from noisy node observations is a central problem in graph signal processing. In this paper, we consider Laplacian-constrained graph estimation for Gaussian Markov random fields, focusing on the underdetermined regime in which the number of samples is smaller than the number of graph nodes. Existing approaches often formulate the problem as a sparsity-regularized maximum-likelihood estimation problem. While effective, such methods typically require iterative optimization and are often computationally demanding, particularly under Laplacian constraints. Instead, we propose a non-iterative estimator of graph Laplacians that uses effective resistance for regularization, and evaluate the method using a simple sparsification procedure. Experiments show that with some trade-off in edge and weight recovery on the considered dataset, computational cost for moderately sized graphs can be substantially reduced.
Journal refIEEE Signal Processing Letters, 2026
