Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers the influence of both graph structure and input features on GNNs. The metrics demonstrate advantages over the commonly used homophily metrics by tests on synthetic graphs. From the metrics and the observations, we find some cases of harmful heterophily can be addressed by diversification operation. With this fact and knowledge of filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to adaptively exploit aggregation, diversification and identity channels in each GNN layer to address harmful heterophily. We validate the ACM-augmented baselines with 10 real-world node classification tasks. They consistently achieve significant performance gain and exceed the state-of-the-art GNNs on most of the tasks without incurring significant computational burden.
Beihang University（北京航空航天大学）；School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；Shen Yuan Honors College, Beihang University（北京航空航天大学沈元荣誉学院）；Hebei University of Technology（河北工业大学）；School of Artificial Intelligence, Hebei University of Technology（河北工业大学人工智能学院）
University of Science and Technology of China（中国科学技术大学）；Baidu Research（百度研究院）；Baidu Inc.（百度公司）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）
最近的工作表明，一种简单、快速的方法，称为简单图卷积（SGC）（Wu et al.，2019），它避开了深度学习，在常见的图机器学习基准测试中与图卷积网络（GCN）（Kipf & Welling，2017）等深度方法具有竞争力。图形数据在SGC中的使用隐含地假设了同质性的共同但不通用的图形特征，其中节点链接到相似的节点。在这里，我们证实了SGC确实对嗜异性（即，非homophilous）图，通过对合成和真实世界数据集的实验。我们提出了自适应简单图卷积（ASGC），我们表明，它可以适应homophilous和heterophilous图结构。像SGC一样，ASGC不是一个深度模型，因此是快速的，可扩展的和可解释的;此外，我们可以证明自然合成数据模型的性能保证。从经验上讲，ASGC通常在现实世界数据集的基准上与最近的深度模型在节点分类方面具有竞争力。SGC论文质疑图神经网络的复杂性是否适用于涉及同构网络的常见图问题;我们的研究结果同样表明，虽然深度学习通常实现最高性能，但异构结构本身并不需要这些更复杂的方法。
HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks
Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts and Telecommunications（江苏大数据安全与智能处理重点实验室，南京邮电大学）；School of Computer Science, Nanjing University of Posts and Telecommunications（计算机科学学院，南京邮电大学）；State Key Laboratory of Novel Software Technology, Nanjing University（新型软件技术国家重点实验室，南京大学）
针对图神经网络的结构不平衡问题，提出 HeRB 方法，先纠正异相性再传递同相知识，通过减少类间边和增加类内边及头尾节点知识传递，在多个基准数据集上取得优越性能。
Addressing Graph Heterogeneity and Heterophily from A Spectral Perspective
Beijing University of Posts and Telecommunications（北京邮电大学）；National University of Singapore（新加坡国立大学）；Beihang University（北京航空航天大学）；Hangzhou Dianzi University（杭州电子科技大学）
Doctoral Program of Computer Science University of Helsinki（赫尔辛基大学计算机科学博士项目）；Research Program in Systems Oncology Faculty of Medicine University of Helsinki（赫尔辛基大学医学学院系统肿瘤研究计划）；Centre for Information Sciences and Systems Nanyang Technological University（南洋理工大学信息科学与系统中心）；University of Montreal（蒙特利尔大学）；Mila Quebec Artificial Intelligence Institute（魁北克人工智能研究所）
Understanding Heterophily for Graph Neural Networks
Beihang University（北京航空航天大学）；School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；Shen Yuan Honors College, Beihang University（北京航空航天大学沈元荣誉学院）；School of Artificial Intelligence, Hebei University of Technology（河北工业大学人工智能学院）
A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions
School of Data Science and Engineering, East China Normal University（华东师范大学数据科学与工程学院）；Microsoft Research Asia（微软亚洲研究院）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）
Graph Neural Networks for Graphs with Heterophily: A Survey
School of Computing Technologies, RMIT University（罗特学院，皇家墨尔本理工大学）；Department of Mathematics, City University of Hong Kong（香港城市大学数学系）；School of Information and Communication Technology, Griffith University（信息与通信技术学院，格里菲斯大学）；Zhejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University（浙江智能教育技术与应用重点实验室，浙江师范大学）；School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen)（计算机科学与技术学院，哈尔滨工业大学（深圳））；School of Computer Science and Technology, Tianjin University（计算机科学与技术学院，天津大学）；Department of Computer Science, University of Illinois at Chicago（计算机科学系，伊利诺伊大学芝加哥分校）
Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger
Beijing University of Posts and Telecommunications（北京邮电大学）；North China Electric Power University（华北电力大学）；University of Kent（肯特大学）；Beihang University（北航）；University of Illinois（伊利诺伊大学）
Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement
Hong Kong Baptist University（香港浸会大学）；Renmin University of China（中国人民大学）；Chinese Academy of Sciences（中国科学院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Sun Yat-sen University（中山大学）
Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks
School of New Media and Communication, Tianjin University（天津大学新媒体与传播学院）；College of Intelligence and Computing, Tianjin University（天津大学智能与计算学院）；Yazhou Bay Innovation Institute, Hainan Tropical Ocean University（海南热带海洋大学亚龙湾创新研究院）；Key Lab of Education Blockchain and Intelligent Technology, Guangxi Normal University（广西师范大学教育区块链与智能技术重点实验室）
Institute of Cyberspace Security, Zhejiang University of Technology（浙江工业大学网络空间安全学院）；Binjiang Institute of Artificial Intelligence（滨江人工智能研究院）；College of Computer Science and Technology, Zhejiang University of Technology（浙江工业大学计算机科学与技术学院）；Science and Technology on Communication Information Security Control Laboratory（通信信息安全控制科学与技术实验室）
