这篇文章后来改名为:Revisiting Graph Neural Networks: Graph Filtering Perspective 投在了2020 25th International Conference on Pattern Recognition (ICPR) 但是相比之下之前的题目更有名,因此本文以Revisiting Graph Neural Networks: All We Have is Low-Pass Filters的版本为主 2.背景动机及贡献 图神经网络是能...
具有较小广义特征值的广义特征向量就变化而言更平滑。因此,广义特征值被称为图的频率 frequency of the graph。 傅里叶部分先跳过,因为还没看懂,反正傅里叶变换就是把特征x(i)经过了某种变换成新的向量,把一个函数变换成一系列正交函数的组合(sin,cos)叠加。 在一个图的机器学习问题中,每个顶点i∈V都有一个d...
2.4 Multiplying Adjacency Matrix is Low Pass Filtering 在大多数图神经网络模型中,信息传播是通过特征矩阵与(增广)邻接矩阵相乘进行的,本节中证明了这种操作对应的正是低通滤波器。 归一化的拉普拉斯矩阵的特征值在[0,2]之间,我们可以增加自环(使用增广邻接矩阵)来增强低通滤波的效果。 定理3:是广义特征值(D~,L...
Convolutional codes,Analytical models,Filtering,Convolution,Graph neural networks,Pattern recognitionIn this work, we develop quantitative results to the learnability of a two-layers Graph Convolutional Network (GCN). Instead of analyzing GCN under some classes of functions, our approach provides a ...
Graph neural networks have become one of the most important techniques to solve machine learning problems on graph-structured data. Recent work on vertex classification proposed deep and distributed learning models to achieve high performance and scalability. However, we find that the feature vectors of...
the graph (G) aggregation ( ˆ A) homophily and its modified version 公式9 Adaptive Channel Mixing (ACM) 这部分是论文的核心内容 在先前的工作[31,8,4]中,已经表明,可以通过高通滤波器(HP)提取的高频图信号在解决异质性方面是经验上有用的。在本节中,基于等式6中的相似度矩阵,我们从理论上证明了多...
Revisiting heterophily for graph neural networks. NIPS, 2022.概介绍了一种新的 graph homophily metrics.符号说明G=(V,E,A)G=(V,E,A), graph; |V|=N|V|=N; A∈RN×NA∈RN×N, adjacency matrix; Ni={j:eij∈E}Ni={j:eij∈E}, neighborhood set; X∈RN×FX∈RN×F, feature matrix; Z...
Revisiting, benchmarking, and refining Heterogeneous Graph Neural Networks. 2023.3.2 update: We make benchmark data including test set pulic. You can download data as follows: Node Classification:https://drive.google.com/drive/folders/10-pf2ADCjq_kpJKFHHLHxr_czNNCJ3aX?usp=sharing ...
近几年异质图GNN(Heterogeneous graph neural networks (HGNNs))颇受关注,但是由于每个工作的数据预处理方式和评估设置都不同,因此很难对新模型具体的进步程度做全面理解。 本文使用12个异质图GNN模型的官方代码、数据集、实验设置和超参,证明了它们毫无进展(也不完全,只能说基本没有)。
simple graph convolutional networks. Second, we propose a residual network structure that is specifically designed for CF with user-item interaction modeling, which alleviates the over smoothing problem in graph convolution aggregation operation with sparse data. The proposed model is a linear model and...