Revisiting Heterophily For Graph Neural Networks

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden.

[1]  Xiang Li,et al.  Finding Global Homophily in Graph Neural Networks When Meeting Heterophily , 2022, ICML.

[2]  Francesco Di Giovanni,et al.  Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs , 2022, NeurIPS.

[3]  Omkar Bhalerao,et al.  Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods , 2021, NeurIPS.

[4]  Sundararajan Sellamanickam,et al.  Simple Truncated SVD based Model for Node Classification on Heterophilic Graphs , 2021, ArXiv.

[5]  Zhewei Wei,et al.  BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation , 2021, NeurIPS.

[6]  Jiliang Tang,et al.  Is Homophily a Necessity for Graph Neural Networks? , 2021, ICLR.

[7]  Derek Lim,et al.  New Benchmarks for Learning on Non-Homophilous Graphs , 2021, ArXiv.

[8]  Kevin Swersky,et al.  Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks , 2021, 2022 IEEE International Conference on Data Mining (ICDM).

[9]  Xiao Wang,et al.  Beyond Low-frequency Information in Graph Convolutional Networks , 2021, AAAI.

[10]  Ryan A. Rossi,et al.  Graph Neural Networks with Heterophily , 2020, AAAI.

[11]  William L. Hamilton Graph Representation Learning , 2020, Synthesis Lectures on Artificial Intelligence and Machine Learning.

[12]  Doina Precup,et al.  Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Networks , 2020, ArXiv.

[13]  Doina Precup,et al.  Training Matters: Unlocking Potentials of Deeper Graph Convolutional Neural Networks , 2020, ArXiv.

[14]  Yaliang Li,et al.  Simple and Deep Graph Convolutional Networks , 2020, ICML.

[15]  L. Akoglu,et al.  Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs , 2020, NeurIPS.

[16]  Olgica Milenkovic,et al.  Adaptive Universal Generalized PageRank Graph Neural Network , 2020, ICLR.

[17]  Shuiwang Ji,et al.  Non-Local Graph Neural Networks , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Rik Sarkar,et al.  Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models , 2020, CIKM.

[19]  Hongzhi Chen,et al.  Measuring and Improving the Use of Graph Information in Graph Neural Networks , 2020, ICLR.

[20]  Kevin Chen-Chuan Chang,et al.  Geom-GCN: Geometric Graph Convolutional Networks , 2020, ICLR.

[21]  Rik Sarkar,et al.  Multi-scale Attributed Node Embedding , 2019, J. Complex Networks.

[22]  Doina Precup,et al.  Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks , 2019, NeurIPS.

[23]  Takanori Maehara,et al.  Revisiting Graph Neural Networks: All We Have is Low-Pass Filters , 2019, ArXiv.

[24]  Kristina Lerman,et al.  MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing , 2019, ICML.

[25]  Jan Eric Lenssen,et al.  Fast Graph Representation Learning with PyTorch Geometric , 2019, ArXiv.

[26]  U. Feige,et al.  Spectral Graph Theory , 2015 .

[27]  Kilian Q. Weinberger,et al.  Simplifying Graph Convolutional Networks , 2019, ICML.

[28]  Stephan Günnemann,et al.  Predict then Propagate: Graph Neural Networks meet Personalized PageRank , 2018, ICLR.

[29]  Ken-ichi Kawarabayashi,et al.  Representation Learning on Graphs with Jumping Knowledge Networks , 2018, ICML.

[30]  Razvan Pascanu,et al.  Relational inductive biases, deep learning, and graph networks , 2018, ArXiv.

[31]  Frank Hutter,et al.  Decoupled Weight Decay Regularization , 2017, ICLR.

[32]  Pietro Liò,et al.  Graph Attention Networks , 2017, ICLR.

[33]  Jure Leskovec,et al.  Inductive Representation Learning on Large Graphs , 2017, NIPS.

[34]  Pierre Vandergheynst,et al.  Geometric Deep Learning: Going beyond Euclidean data , 2016, IEEE Signal Process. Mag..

[35]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[36]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[37]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[38]  Yoshua Bengio,et al.  Neural Machine Translation by Jointly Learning to Align and Translate , 2014, ICLR.

[39]  Geoffrey E. Hinton,et al.  Speech recognition with deep recurrent neural networks , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[40]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[41]  W. Kittisupamongkol Two sides of the same coin? , 2010, Singapore medical journal.

[42]  Peter Vary,et al.  An adaptive filter-bank equalizer for speech enhancement , 2006, Signal Process..

[43]  M. McPherson,et al.  Birds of a Feather: Homophily in Social Networks , 2001 .

[44]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[45]  Venkatesan N. Ekambaram Graph Structured Data Viewed Through a Fourier Lens , 2013 .

[46]  Ah Chung Tsoi,et al.  The Graph Neural Network Model , 2009, IEEE Transactions on Neural Networks.

[47]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.