论文标题
分层图光谱
Stratified Graph Spectra
论文作者
论文摘要
在经典的图形信号处理中，给定具有实值的图形信号，其图形傅立叶变换通常定义为laplacian的信号和每个特征向量之间的一系列内部产物。不幸的是，在矢量值图表信号的情况下，该定义在数学上无效，但是在最新的图形学习建模和分析中是典型的操作数。因此，寻求广泛的转换解码矢量值信号的特征组件的大小是本文的主要目的。探索了几次尝试，并且还发现在邻接的层次级别执行转换有助于更深入地介绍信号的光谱特征。提出的方法是作为一种新工具引入，可帮助诊断和分析图模型的概况。
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this definition is not mathematically valid in the cases of vector-valued graph signals which however are typical operands in the state-of-the-art graph learning modeling and analyses. Seeking a generalized transformation decoding the magnitudes of eigencomponents from vector-valued signals is thus the main objective of this paper. Several attempts are explored, and also it is found that performing the transformation at hierarchical levels of adjacency help profile the spectral characteristics of signals more insightfully. The proposed methods are introduced as a new tool assisting on diagnosing and profiling behaviors of graph learning models.
