论文标题
使用定向变化的无限和复杂图的图形信号处理
Graph Signal Processing of Indefinite and Complex Graphs using Directed Variation
论文作者
论文摘要
在图形信号处理（GSP）的领域，有向图为GSP的“标准方法”提出了特定的挑战，因为它们的不对称性质。负面或复杂的定向边缘的存在，这是一种用于神经科学，关键基础设施和机器人协调等领域中的图形结构，使问题进一步复杂化。最近的结果将图形信号的总变化概括为定向变化，这是开发图形傅立叶变换（GFT）的激励原理。在这里，我们将这些技术扩展到适用于无限和复杂值图的信号变化的概念，并使用它们为这些类别的图形定义GFT。提出了随机图上的模拟结果，以及对果蝇连接组的一部分的案例研究。
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical structure used in fields such as neuroscience, critical infrastructure, and robot coordination, further complicates the issue. Recent results generalized the total variation of a graph signal to that of directed variation as a motivating principle for developing a graphical Fourier transform (GFT). Here, we extend these techniques to concepts of signal variation appropriate for indefinite and complex-valued graphs and use them to define a GFT for these classes of graph. Simulation results on random graphs are presented, as well as a case study of a portion of the fruit fly connectome.
