论文标题
社区感知的图形信号处理
Community-Aware Graph Signal Processing
论文作者
论文摘要
图形信号处理（GSP）的新兴场允许将经典信号处理操作（例如过滤）转换为图上的信号。 GSP框架通常建立在图形laplacian上，该图对于研究图形特性和测量图信号平滑度起着至关重要的作用。相反，我们将图形模块矩阵作为GSP的核心，以在图表上处理信号时结合有关图形群落结构的知识，但无需社区检测。我们在多种通用设置中研究这种方法，例如过滤，最佳采样和重建，替代数据生成和降解。一个小规模的示例和一个运输网络数据集说明了可行性，以及在人类神经影像中的一个应用，在该应用程序中，社区意识到的GSP揭示了行为与基于Laplacian的GSP未显示的行为与大脑特征之间的关系。这项工作表明了网络科学的概念如何导致图形信号上的新有意义的操作。
The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role to study graph properties and measure graph signal smoothness. Here instead, we propose the graph modularity matrix as the centerpiece of GSP, in order to incorporate knowledge about graph community structure when processing signals on the graph, but without the need for community detection. We study this approach in several generic settings such as filtering, optimal sampling and reconstruction, surrogate data generation, and denoising. Feasibility is illustrated by a small-scale example and a transportation network dataset, as well as one application in human neuroimaging where community-aware GSP reveals relationships between behavior and brain features that are not shown by Laplacian-based GSP. This work demonstrates how concepts from network science can lead to new meaningful operations on graph signals.
