论文标题
光谱图分数傅立叶变换用于有向图及其应用
Spectral graph fractional Fourier transform for directed graphs and its application
论文作者
论文摘要
在图形信号处理中，许多研究认为基础网络是无方向性的。尽管Digraph模型很少采用，但它更适合许多应用程序，尤其是对于现实世界网络。在本文中，我们提出了一个通用框架，用于将图形信号处理扩展到图分数域中的有向图。为此，我们考虑了有向图上的分数Hermitian laplacian矩阵的新定义，并将光谱图分数傅立叶变换推广到有向图（DGFRFT）。基于我们的新变换，我们定义过滤，该过滤用于减少在温度数据上叠加的不必要的噪声。最后，还通过使用现实世界的有向图进行数值实验来评估所提出的DGFRFT方法的性能。
In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Hermitian Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used in reducing unnecessary noise superimposed on temperature data. Finally, the performance of the proposed DGFRFT approach is also evaluated through numerical experiments using real-world directed graphs.
