社区感知图信号处理
Community-Aware Graph Signal Processing
摘要：
图形信号处理（GSP）的新兴领域允许转置经典的信号处理操作（例如，滤波）到图上的信号。GSP框架通常建立在图拉普拉斯算子的基础上，它在研究图的性质和测量图信号的平滑性方面起着至关重要的作用。在这里，我们提出了图模块化矩阵作为GSP的核心，以便在处理图上的信号时纳入有关图社区结构的知识，但不需要社区检测。我们研究这种方法在几个通用的设置，如过滤，最佳采样和重建，替代数据生成，和去噪。可行性说明了一个小规模的例子和交通网络数据集，以及在人类神经成像的一个应用程序，其中社区意识的GSP揭示行为和大脑功能之间的关系，不显示基于拉普拉斯的GSP。这项工作展示了网络科学的概念如何在图形信号上产生新的有意义的操作。
英文摘要：
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.
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