联合优化图结构与采样点选择，提升信号重建效率。
Towards joint graph learning and sampling set selection from data
- 从图学习中提取节点重要性，指导采样集生成
- 所提方法在模拟数据上重建精度相当且计算开销更低
- 适合需高效采样的动态图信号场景
我们研究了图结构未预先定义、需从数据中推断的图信号采样问题。现有方法多采用两步流程：先学习图结构，再进行采样。本文提出一种联合优化框架，核心为顶点重要性采样（VIS），通过图学习得到的节点权重确定采样集。进一步提出带排斥机制的顶点重要性采样（VISR），以确保选出的空间分离的高重要性节点，提升重构性能。在模拟数据上的实验表明，使用VIS和VISR进行采样，在重建性能与计算复杂度方面均优于传统两步法。
原文摘要 · Abstract (English)
We explore the problem of sampling graph signals in scenarios where the graph structure is not predefined and must be inferred from data. In this scenario, existing approaches rely on a two-step process, where a graph is learned first, followed by sampling. More generally, graph learning and graph signal sampling have been studied as two independent problems in the literature. This work provides a foundational step towards jointly optimizing the graph structure and sampling set. Our main contribution, Vertex Importance Sampling (VIS), is to show that the sampling set can be effectively determined from the vertex importance (node weights) obtained from graph learning. We further propose Vertex Importance Sampling with Repulsion (VISR), a greedy algorithm where spatially -separated "important" nodes are selected to ensure better reconstruction. Empirical results on simulated data show that sampling using VIS and VISR leads to competitive reconstruction performance and lower complexity than the conventional two-step approach of graph learning followed by graph sampling.
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