Title: Node-Variant Graph Filters in Graph Neural Networks Show Chinese title

Title: 节点变体图滤波器在图神经网络中的应用

Abstract: Graph neural networks (GNNs) have been successfully employed in a myriad of applications involving graph signals. Theoretical findings establish that GNNs use nonlinear activation functions to create low-eigenvalue frequency content that can be processed in a stable manner by subsequent graph convolutional filters. However, the exact shape of the frequency content created by nonlinear functions is not known and cannot be learned. In this work, we use node-variant graph filters (NVGFs) -- which are linear filters capable of creating frequencies -- as a means of investigating the role that frequency creation plays in GNNs. We show that, by replacing nonlinear activation functions by NVGFs, frequency creation mechanisms can be designed or learned. By doing so, the role of frequency creation is separated from the nonlinear nature of traditional GNNs. Simulations on graph signal processing problems are carried out to pinpoint the role of frequency creation. Show Chinese abstract

Abstract: 图神经网络（GNNs）已被成功应用于涉及图信号的众多应用中。理论研究结果表明，GNNs 使用非线性激活函数来创建低特征值频率内容，这些内容可以被后续的图卷积滤波器以稳定的方式处理。然而，非线性函数创建的频率内容的确切形状是未知的且无法学习。在本工作中，我们使用节点变体图滤波器（NVGFs）——这些是能够创建频率的线性滤波器——作为研究频率创建在GNNs中作用的一种手段。我们证明，通过将非线性激活函数替换为NVGFs，可以设计或学习频率创建机制。这样做，将频率创建的作用与传统GNNs的非线性特性分离开来。在图信号处理问题上进行的仿真旨在明确频率创建的作用。