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图神经网络深度解析：想要了解图或图神经网络

小君 83

图神经网络深度解析：想要了解图或图神经网络例如 GNN 可以表示子图的语义信息，将网络中一小部分节点构成的语义表示出来，这是以前 Graph Embedding 不容易做到的。GNN 还可以在整个图网络上进行信息传播、聚合等建模，也就是说它可以把图网络当成一个整体进行建模。此外，GNN 对单个节点的表示也可以做得更好，因为它可以更好地建模周围节点丰富信息。Graph Embedding 算法聚焦在如何对网络节点进行低维向量表示，相似的节点在表征空间中更加接近。相比之下，GNN 最大的优势在于它不只可以对一个节点进行语义表示。但图这种结构化数据有个麻烦的地方，我们先要有图才能进行后续的计算。但图的搭建并不简单，目前也没有比较好的自动化方法，所以第一步还是需要挺多功夫的。只要各节点及边都确定了，那么图就是一种非常强大且复杂的工具，模型也能推断出图中的各种隐藏知识。不同时期的图建模其实，我们可以将图建模分为图神经网络与传统的图模型。其中

机器之心编辑

参与：思源

图嵌入、图表征、图分类、图神经网络，这篇文章将介绍你需要的图建模论文，当然它们都有配套实现的。

图是一种非常神奇的表示方式，生活中绝大多数的现象或情境都能用图来表示，例如人际关系网、道路交通网、信息互联网等等。正如马哲介绍事物具有普遍联系性，而图正好能捕捉这种联系，所以用它来描述这个世界是再好不过的方法。

但图这种结构化数据有个麻烦的地方，我们先要有图才能进行后续的计算。但图的搭建并不简单，目前也没有比较好的自动化方法，所以第一步还是需要挺多功夫的。只要各节点及边都确定了，那么图就是一种非常强大且复杂的工具，模型也能推断出图中的各种隐藏知识。

图神经网络深度解析：想要了解图或图神经网络(1)

不同时期的图建模

其实，我们可以将图建模分为图神经网络与传统的图模型。其中以前的图建模主要借助 Graph Embedding 为不同的节点学习低维向量表征，这借鉴了 NLP 中词嵌入的思想。而图神经网络借助深度学习进行更强大的图运算与图表征。

Graph Embedding 算法聚焦在如何对网络节点进行低维向量表示，相似的节点在表征空间中更加接近。相比之下，GNN 最大的优势在于它不只可以对一个节点进行语义表示。

例如 GNN 可以表示子图的语义信息，将网络中一小部分节点构成的语义表示出来，这是以前 Graph Embedding 不容易做到的。GNN 还可以在整个图网络上进行信息传播、聚合等建模，也就是说它可以把图网络当成一个整体进行建模。此外，GNN 对单个节点的表示也可以做得更好，因为它可以更好地建模周围节点丰富信息。

在传统图建模中，随机游走、最短路径等图方法会利用符号知识，但这些方法并没有办法很好地利用每个节点的语义信息。而深度学习技术更擅长处理非结构文本、图像等数据。简言之，我们可以将 GNN 看做将深度学习技术应用到符号表示的图数据上，或者说是从非结构化数据扩展到了结构化数据。GNN 能够充分融合符号表示和低维向量表示，发挥两者优势。

图建模论文与代码

在 GitHub 的一项开源工作中，开发者收集了图建模相关的论文与实现，并且从经典的 Graph Embedding、Graph Kernel 到图神经网络都有涉及。它们在图嵌入、图分类、图表征等领域都是非常重要的论文。

项目地址：https://github.com/benedekrozemberczki/awesome-graph-classification

该项目主要收集的论文领域如下所示：

1. Factorization

2. Spectral and Statistical Fingerprints

3. Graph Neural Network

4. Graph Kernels

因式分解法

  • Learning Graph Representation via Frequent Subgraphs (SDM 2018)
  • Dang Nguyen Wei Luo Tu Dinh Nguyen Svetha Venkatesh Dinh Phung
  • Paper：https://epubs.siam.org/doi/10.1137/1.9781611975321.35
  • Python：https://github.com/nphdang/GE-FSG
  • Anonymous Walk Embeddings (ICML 2018)
  • Sergey Ivanov and Evgeny Burnaev
  • Paper：https://arxiv.org/pdf/1805.11921.pdf
  • Python：https://github.com/nd7141/AWE
  • Graph2vec (MLGWorkshop 2017)
  • Annamalai Narayanan Mahinthan Chandramohan Lihui Chen Yang Liu and Santhoshkumar Saminathan
  • Paper：https://arxiv.org/abs/1707.05005
  • Python High Performance：https://github.com/benedekrozemberczki/graph2vec
  • Python Reference：https://github.com/MLDroid/graph2vec_tf
  • Subgraph2vec (MLGWorkshop 2016)
  • Annamalai Narayanan Mahinthan Chandramohan Lihui Chen Yang Liu and Santhoshkumar Saminathan
  • Paper：https://arxiv.org/abs/1606.08928
  • Python High Performance：https://github.com/MLDroid/subgraph2vec_gensim
  • Python Reference：https://github.com/MLDroid/subgraph2vec_tf
  • Rdf2Vec: RDF Graph Embeddings for Data Mining (ISWC 2016)
  • Petar Ristoski and Heiko Paulheim
  • Paper：https://link.springer.com/chapter/10.1007/978-3-319-46523-4_30
  • Python Reference：https://github.com/airobert/RDF2VecAtWebScale
  • Deep Graph Kernels (KDD 2015)
  • Pinar Yanardag and S.V.N. Vishwanathan
  • Paper：https://dl.acm.org/citation.cfm?id=2783417
  • Python Reference：https://github.com/pankajk/Deep-Graph-Kernels

Spectral and Statistical Fingerprints

  • A Simple Yet Effective Baseline for Non-Attribute Graph Classification (ICLR RLPM 2019)
  • Chen Cai Yusu Wang
  • Paper：https://arxiv.org/abs/1811.03508
  • Python Reference：https://github.com/Chen-Cai-OSU/LDP
  • NetLSD (KDD 2018)
  • Anton Tsitsulin Davide Mottin Panagiotis Karras Alex Bronstein and Emmanuel Müller
  • Paper：https://arxiv.org/abs/1805.10712
  • Python Reference：https://github.com/xgfs/NetLSD
  • A Simple Baseline Algorithm for Graph Classification (Relational Representation Learning NIPS 2018)
  • Nathan de Lara and Edouard Pineau
  • Paper：https://arxiv.org/pdf/1810.09155.pdf
  • Python Reference：https://github.com/edouardpineau/A-simple-baseline-algorithm-for-graph-classification
  • Multi-Graph Multi-Label Learning Based on Entropy (Entropy NIPS 2018)
  • Zixuan Zhu and Yuhai Zhao
  • Paper：https://github.com/TonyZZX/MultiGraph_MultiLabel_Learning/blob/master/entropy-20-00245.pdf
  • Python Reference：https://github.com/TonyZZX/MultiGraph_MultiLabel_Learning
  • Hunt For The Unique Stable Sparse And Fast Feature Learning On Graphs (NIPS 2017)
  • Saurabh Verma and Zhi-Li Zhang
  • Paper：https://papers.nips.cc/paper/6614-hunt-for-the-unique-stable-sparse-and-fast-feature-learning-on-graphs.pdf
  • Python Reference：https://github.com/vermaMachineLearning/FGSD
  • Joint Structure Feature Exploration and Regularization for Multi-Task Graph Classification (TKDE 2015)
  • Shirui Pan Jia Wu Xingquan Zhuy Chengqi Zhang and Philip S. Yuz
  • Paper：https://ieeexplore.ieee.org/document/7302040
  • Java Reference：https://github.com/shiruipan/MTG
  • NetSimile: A Scalable Approach to Size-Independent Network Similarity (arXiv 2012)
  • Michele Berlingerio Danai Koutra Tina Eliassi-Rad and Christos Faloutsos
  • Paper：https://arxiv.org/abs/1209.2684
  • Python：https://github.com/kristyspatel/Netsimile

图神经网络

  • Self-Attention Graph Pooling (ICML 2019)
  • Junhyun Lee Inyeop Lee Jaewoo Kang
  • Paper：https://arxiv.org/abs/1904.08082
  • Python Reference：https://github.com/inyeoplee77/SAGPool
  • Variational Recurrent Neural Networks for Graph Classification (ICLR 2019)
  • Edouard Pineau Nathan de Lara
  • Paper：https://arxiv.org/abs/1902.02721
  • Python Reference：https://github.com/edouardpineau/Variational-Recurrent-Neural-Networks-for-Graph-Classification
  • Crystal Graph Neural Networks for Data Mining in Materials Science (Arxiv 2019)
  • Takenori Yamamoto
  • Paper：https://storage.googleapis.com/rimcs_cgnn/cgnn_matsci_May_27_2019.pdf
  • Python Reference：https://github.com/Tony-Y/cgnn
  • Explainability Techniques for Graph Convolutional Networks (ICML 2019)
  • Federico Baldassarre Hossein Azizpour
  • Paper：https://128.84.21.199/pdf/1905.13686.pdf
  • Python Reference：https://github.com/gn-exp/gn-exp
  • Semi-Supervised Graph Classification: A Hierarchical Graph Perspective (WWW 2019)
  • Jia Li Yu Rong Hong Cheng Helen Meng Wenbing Huang and Junzhou Huang
  • Paper：https://arxiv.org/pdf/1904.05003.pdf
  • Python Reference：https://github.com/benedekrozemberczki/SEAL-CI
  • Capsule Graph Neural Network (ICLR 2019)
  • Zhang Xinyi and Lihui Chen
  • Paper：https://openreview.net/forum?id=Byl8BnRcYm
  • Python Reference：https://github.com/benedekrozemberczki/CapsGNN
  • How Powerful are Graph Neural Networks? (ICLR 2019)
  • Keyulu Xu Weihua Hu Jure Leskovec Stefanie Jegelka
  • Paper：https://arxiv.org/abs/1810.00826
  • Python Reference：https://github.com/weihua916/powerful-gnns
  • Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks (AAAI 2019)
  • Christopher Morris Martin Ritzert Matthias Fey William L. Hamilton Jan Eric Lenssen Gaurav Rattan and Martin Grohe
  • Paper：https://arxiv.org/pdf/1810.02244v2.pdf
  • Python Reference：https://github.com/k-gnn/k-gnn
  • Capsule Neural Networks for Graph Classification using Explicit Tensorial Graph Representations (Arxiv 2019)
  • Marcelo Daniel Gutierrez Mallea Peter Meltzer and Peter J Bentley
  • Paper：https://arxiv.org/pdf/1902.08399v1.pdf
  • Python Reference：https://github.com/BraintreeLtd/PatchyCapsules
  • Three-Dimensionally Embedded Graph Convolutional Network for Molecule Interpretation (Arxiv 2018)
  • Hyeoncheol Cho and Insung. S. Choi
  • Paper：https://arxiv.org/abs/1811.09794
  • Python Reference：https://github.com/blackmints/3DGCN
  • Learning Graph-Level Representations with Recurrent Neural Networks (Arxiv 2018)
  • Yu Jin and Joseph F. JaJa
  • Paper：https://arxiv.org/pdf/1805.07683v4.pdf
  • Python Reference：https://github.com/yuj-umd/graphRNN
  • Graph Capsule Convolutional Neural Networks (ICML 2018)
  • Saurabh Verma and Zhi-Li Zhang
  • Paper：https://arxiv.org/abs/1805.08090
  • Python Reference：https://github.com/vermaMachineLearning/Graph-Capsule-CNN-Networks
  • Graph Classification Using Structural Attention (KDD 2018)
  • John Boaz Lee Ryan Rossi and Xiangnan Kong
  • Paper：http://ryanrossi.com/pubs/KDD18-graph-attention-model.pdf
  • Python Pytorch Reference：https://github.com/benedekrozemberczki/GAM
  • Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation (NIPS 2018)
  • Jiaxuan You Bowen Liu Rex Ying Vijay Pande and Jure Leskovec
  • Paper：https://arxiv.org/abs/1806.02473
  • Python Reference：https://github.com/bowenliu16/rl_graph_generation
  • Hierarchical Graph Representation Learning with Differentiable Pooling (NIPS 2018)
  • Zhitao Ying Jiaxuan You Christopher Morris Xiang Ren Will Hamilton and Jure Leskovec
  • Paper：http://papers.nips.cc/paper/7729-hierarchical-graph-representation-learning-with-differentiable-pooling.pdf
  • Python Reference：https://github.com/rusty1s/pytorch_geometric
  • Contextual Graph Markov Model: A Deep and Generative Approach to Graph Processing (ICML 2018)
  • Davide Bacciu Federico Errica and Alessio Micheli
  • Paper：https://arxiv.org/pdf/1805.10636.pdf
  • Python Reference：https://github.com/diningphil/CGMM
  • MolGAN: An Implicit Generative Model for Small Molecular Graphs (ICML 2018)
  • Nicola De Cao and Thomas Kipf
  • Paper：https://arxiv.org/pdf/1805.11973.pdf
  • Python Reference：https://github.com/nicola-decao/MolGAN
  • Deeply Learning Molecular Structure-Property Relationships Using Graph Attention Neural Network (2018)
  • Seongok Ryu Jaechang Lim and Woo Youn Kim
  • Paper：https://arxiv.org/abs/1805.10988
  • Python Reference：https://github.com/SeongokRyu/Molecular-GAT
  • Compound-protein Interaction Prediction with End-to-end Learning of Neural Networks for Graphs and Sequences (Bioinformatics 2018)
  • Masashi Tsubaki Kentaro Tomii and Jun Sese
  • Paper：https://academic.oup.com/bioinformatics/article/35/2/309/5050020
  • Python Reference：https://github.com/masashitsubaki/CPI_prediction
  • Python Reference：https://github.com/masashitsubaki/GNN_molecules
  • Python Alternative：https://github.com/xnuohz/GCNDTI
  • Learning Graph Distances with Message Passing Neural Networks (ICPR 2018)
  • Pau Riba Andreas Fischer Josep Llados and Alicia Fornes
  • Paper：https://ieeexplore.ieee.org/abstract/document/8545310
  • Python Reference：https://github.com/priba/siamese_ged
  • Edge Attention-based Multi-Relational Graph Convolutional Networks (2018)
  • Chao Shang Qinqing Liu Ko-Shin Chen Jiangwen Sun Jin Lu Jinfeng Yi and Jinbo Bi
  • Paper：https://arxiv.org/abs/1802.04944v1
  • Python Reference：https://github.com/Luckick/EAGCN
  • Commonsense Knowledge Aware Conversation Generation with Graph Attention (IJCAI-ECAI 2018)
  • Hao Zhou Tom Yang Minlie Huang Haizhou Zhao Jingfang Xu and Xiaoyan Zhu
  • Paper：http://coai.cs.tsinghua.edu.cn/hml/media/files/2018_commonsense_ZhouHao_3_TYVQ7Iq.pdf
  • Python Reference：https://github.com/tuxchow/ccm
  • Residual Gated Graph ConvNets (ICLR 2018)
  • Xavier Bresson and Thomas Laurent
  • Paper：https://arxiv.org/pdf/1711.07553v2.pdf
  • Python Pytorch Reference：https://github.com/xbresson/spatial_graph_convnets
  • An End-to-End Deep Learning Architecture for Graph Classification (AAAI 2018)
  • Muhan Zhang Zhicheng Cui Marion Neumann and Yixin Chen
  • Paper：https://www.cse.wustl.edu/~muhan/papers/AAAI_2018_DGCNN.pdf
  • Python Tensorflow Reference：https://github.com/muhanzhang/DGCNN
  • Python Pytorch Reference：https://github.com/muhanzhang/pytorch_DGCNN
  • MATLAB Reference：https://github.com/muhanzhang/DGCNN
  • Python Alternative：https://github.com/leftthomas/DGCNN
  • Python Alternative：https://github.com/hitlic/DGCNN-tensorflow
  • SGR: Self-Supervised Spectral Graph Representation Learning (KDD DLDay 2018)
  • Anton Tsitsulin Davide Mottin Panagiotis Karra Alex Bronstein and Emmanueal Müller
  • Paper：https://arxiv.org/abs/1807.02839
  • Python Reference：http://mott.in/publications/others/sgr/
  • Deep Learning with Topological Signatures (NIPS 2017)
  • Christoph Hofer Roland Kwitt Marc Niethammer and Andreas Uhl
  • paper：https://arxiv.org/abs/1707.04041
  • Python Reference：https://github.com/c-hofer/nips2017
  • Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (CVPR 2017)
  • Martin Simonovsky and Nikos Komodakis
  • paper：https://arxiv.org/pdf/1704.02901v3.pdf
  • Python Reference：https://github.com/mys007/ecc
  • Deriving Neural Architectures from Sequence and Graph Kernels (ICML 2017)
  • Tao Lei Wengong Jin Regina Barzilay and Tommi Jaakkola
  • Paper：https://arxiv.org/abs/1705.09037
  • Python Reference：https://github.com/taolei87/icml17_knn
  • Protein Interface Prediction using Graph Convolutional Networks (NIPS 2017)
  • Alex Fout Jonathon Byrd Basir Shariat and Asa Ben-Hur
  • Paper：https://papers.nips.cc/paper/7231-protein-interface-prediction-using-graph-convolutional-networks
  • Python Reference：https://github.com/fouticus/pipgcn
  • Graph Classification with 2D Convolutional Neural Networks (2017)
  • Antoine J.-P. Tixier Giannis Nikolentzos Polykarpos Meladianos and Michalis Vazirgiannis
  • Paper：https://arxiv.org/abs/1708.02218
  • Python Reference：https://github.com/Tixierae/graph_2D_CNN
  • CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters (IEEE TSP 2017)
  • Ron Levie Federico Monti Xavier Bresson Michael M. Bronstein
  • Paper：https://arxiv.org/pdf/1705.07664v2.pdf
  • Python Reference：https://github.com/fmonti/CayleyNet
  • Semi-supervised Learning of Hierarchical Representations of Molecules Using Neural Message Passing (2017)
  • Hai Nguyen Shin-ichi Maeda Kenta Oono
  • Paper：https://arxiv.org/pdf/1711.10168.pdf
  • Python Reference：https://github.com/pfnet-research/hierarchical-molecular-learning
  • Kernel Graph Convolutional Neural Networks (2017)
  • Giannis Nikolentzos Polykarpos Meladianos Antoine Jean-Pierre Tixier Konstantinos Skianis Michalis Vazirgiannis
  • Paper：https://arxiv.org/pdf/1710.10689.pdf
  • Python Reference：https://github.com/giannisnik/cnn-graph-classification
  • Deep Topology Classification: A New Approach For Massive Graph Classification (IEEE Big Data 2016)
  • Stephen Bonner John Brennan Georgios Theodoropoulos Ibad Kureshi Andrew Stephen McGough
  • Paper：https://ieeexplore.ieee.org/document/7840988/
  • Python Reference：https://github.com/sbonner0/DeepTopologyClassification
  • Learning Convolutional Neural Networks for Graphs (ICML 2016)
  • Mathias Niepert Mohamed Ahmed Konstantin Kutzkov
  • Paper：https://arxiv.org/abs/1605.05273
  • Python Reference：https://github.com/tvayer/PSCN
  • Gated Graph Sequence Neural Networks (ICLR 2016)
  • Yujia Li Daniel Tarlow Marc Brockschmidt Richard Zemel
  • Paper：https://arxiv.org/abs/1511.05493
  • Python TensorFlow：https://github.com/bdqnghi/ggnn.tensorflow
  • Python PyTorch：https://github.com/JamesChuanggg/ggnn.pytorch
  • Python Reference：https://github.com/YunjaeChoi/ggnnmols
  • Convolutional Networks on Graphs for Learning Molecular Fingerprints (NIPS 2015)
  • David Duvenaud Dougal Maclaurin Jorge Aguilera-Iparraguirre Rafael Gómez-Bombarelli Timothy Hirzel Alán Aspuru-Guzik and Ryan P. Adams
  • Paper：https://papers.nips.cc/paper/5954-convolutional-networks-on-graphs-for-learning-molecular-fingerprints.pdf
  • Python Reference：https://github.com/fllinares/neural_fingerprints_tf
  • Python Reference：https://github.com/jacklin18/neural-fingerprint-in-GNN
  • Python Reference：https://github.com/HIPS/neural-fingerprint
  • Python Reference：https://github.com/debbiemarkslab/neural-fingerprint-theano

Graph Kernels

  • Message Passing Graph Kernels (2018)
  • Giannis Nikolentzos Michalis Vazirgiannis
  • Paper：https://arxiv.org/pdf/1808.02510.pdf
  • Python Reference：https://github.com/giannisnik/message_passing_graph_kernels
  • Matching Node Embeddings for Graph Similarity (AAAI 2017)
  • Giannis Nikolentzos Polykarpos Meladianos and Michalis Vazirgiannis
  • Paper：https://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14494
  • Global Weisfeiler-Lehman Graph Kernels (2017)
  • Christopher Morris Kristian Kersting and Petra Mutzel
  • Paper：https://arxiv.org/pdf/1703.02379.pdf
  • C Reference：https://github.com/chrsmrrs/glocalwl
  • On Valid Optimal Assignment Kernels and Applications to Graph Classification (2016)
  • Nils Kriege Pierre-Louis Giscard Richard Wilson
  • Paper：https://arxiv.org/pdf/1606.01141.pdf
  • Java Reference：https://github.com/nlskrg/optimal_assignment_kernels
  • Efficient Comparison of Massive Graphs Through The Use Of ‘Graph Fingerprints’ (MLGWorkshop 2016)
  • Stephen Bonner John Brennan and A. Stephen McGough
  • Paper：http://dro.dur.ac.uk/19773/1/19773.pdf?DDD10 lzdh59 d700tmt
  • python Reference：https://github.com/sbonner0/GraphFingerprintComparison
  • The Multiscale Laplacian Graph Kernel (NIPS 2016)
  • Risi Kondor and Horace Pan
  • Paper：https://arxiv.org/abs/1603.06186
  • C Reference：https://github.com/horacepan/MLGkernel
  • Faster Kernels for Graphs with Continuous Attributes (ICDM 2016)
  • Christopher Morris Nils M. Kriege Kristian Kersting and Petra Mutzel
  • Paper：https://arxiv.org/abs/1610.00064
  • Python Reference：https://github.com/chrsmrrs/hashgraphkernel
  • Propagation Kernels: Efficient Graph Kernels From Propagated Information (Machine Learning 2016)
  • Neumann Marion and Garnett Roman and Bauckhage Christian and Kersting Kristian
  • Paper：https://link.springer.com/article/10.1007/s10994-015-5517-9
  • Matlab Reference：https://github.com/marionmari/propagation_kernels
  • Halting Random Walk Kernels (NIPS 2015)
  • Mahito Sugiyama and Karsten M. Borgward
  • Paper：https://pdfs.semanticscholar.org/79ba/8bcfbf9496834fdc22a1f7c96d26d776cd6c.pdf
  • C Reference：https://github.com/BorgwardtLab/graph-kernels
  • Scalable Kernels for Graphs with Continuous Attributes (NIPS 2013)
  • Aasa Feragen Niklas Kasenburg Jens Petersen Marleen de Bruijne and Karsten Borgwardt
  • Paper：https://papers.nips.cc/paper/5155-scalable-kernels-for-graphs-with-continuous-attributes.pdf
  • Subgraph Matching Kernels for Attributed Graphs (ICML 2012)
  • Nils Kriege and Petra Mutzel
  • Paper：https://arxiv.org/abs/1206.6483
  • Python Reference：https://github.com/mockingbird2/GraphKernelBenchmark
  • Nested Subtree Hash Kernels for Large-Scale Graph Classification over Streams (ICDM 2012)
  • Bin Li Xingquan Zhu Lianhua Chi Chengqi Zhang
  • Paper：https://ieeexplore.ieee.org/document/6413884/
  • Python Reference：https://github.com/benedekrozemberczki/NestedSubtreeHash
  • Weisfeiler-Lehman Graph Kernels (JMLR 2011)
  • Nino Shervashidze Pascal Schweitzer Erik Jan van Leeuwen Kurt Mehlhorn and Karsten M. Borgwardt
  • Paper：http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf
  • Python Reference：https://github.com/jajupmochi/py-graph
  • Python Reference：https://github.com/deeplego/wl-graph-kernels
  • C Reference：https://github.com/BorgwardtLab/graph-kernels
  • Fast Neighborhood Subgraph Pairwise Distance Kernel (ICML 2010)
  • Fabrizio Costa and Kurt De Grave
  • Paper：https://icml.cc/Conferences/2010/papers/347.pdf
  • C Reference：https://github.com/benedekrozemberczki/awesome-graph-classification/blob/master/www.bioinf.uni-freiburg.de/~costa/EDeNcpp.tgz
  • Python Reference：https://github.com/fabriziocosta/EDeN
  • A Linear-time Graph Kernel (ICDM 2009)
  • Shohei Hido and Hisashi Kashima
  • Paper：https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5360243
  • Python Reference：https://github.com/hgascon/adagio
  • Weisfeiler-Lehman Subtree Kernels (NIPS 2009)
  • Nino Shervashidze Pascal Schweitzer Erik Jan van Leeuwen Kurt Mehlhorn and Karsten M. Borgwardt
  • Paper：http://papers.nips.cc/paper/3813-fast-subtree-kernels-on-graphs.pdf
  • Python Reference：https://github.com/jajupmochi/py-graph
  • Python Reference：https://github.com/deeplego/wl-graph-kernels
  • C Reference：https://github.com/BorgwardtLab/graph-kernels
  • Fast Computation of Graph Kernels (NIPS 2006)
  • S. V. N. Vishwanathan Karsten M. Borgwardt and Nicol N. Schraudolph
  • Paper：http://www.dbs.ifi.lmu.de/Publikationen/Papers/VisBorSch06.pdf
  • Python Reference：https://github.com/jajupmochi/py-graph
  • C Reference：https://github.com/BorgwardtLab/graph-kernels
  • Shortest-Path Kernels on Graphs (ICDM 2005)
  • Karsten M. Borgwardt and Hans-Peter Kriegel
  • Paper：https://www.ethz.ch/content/dam/ethz/special-interest/bsse/borgwardt-lab/documents/papers/BorKri05.pdf
  • C Reference：https://github.com/KitwareMedical/ITKTubeTK
  • Cyclic Pattern Kernels For Predictive Graph Mining (KDD 2004)
  • Tamás Horváth Thomas Gärtner and Stefan Wrobel
  • Paper：http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.332.6158&rep=rep1&type=pdf
  • Python Reference：https://github.com/jajupmochi/py-graph
  • Extensions of Marginalized Graph Kernels (ICML 2004)
  • Pierre Mahe Nobuhisa Ueda Tatsuya Akutsu Jean-Luc Perret and Jean-Philippe Vert
  • Paper：http://members.cbio.mines-paristech.fr/~jvert/publi/04icml/icmlMod.pdf
  • Python Reference：https://github.com/jajupmochi/py-graph
  • Marginalized Kernels Between Labeled Graphs (ICML 2003)
  • Hisashi Kashima Koji Tsuda and Akihiro Inokuchi
  • Paper：https://pdfs.semanticscholar.org/2dfd/92c808487049ab4c9b45db77e9055b9da5a2.pdf
  • Python Reference：https://github.com/jajupmochi/py-graph

不同时期的图建模

其实，我们可以将图建模分为图神经网络与传统的图模型。其中以前的图建模主要借助 Graph Embedding 为不同的节点学习低维向量表征，这借鉴了 NLP 中词嵌入的思想。而图神经网络借助深度学习进行更强大的图运算与图表征。

Graph Embedding 算法聚焦在如何对网络节点进行低维向量表示，相似的节点在表征空间中更加接近。相比之下，GNN 最大的优势在于它不只可以对一个节点进行语义表示。

例如 GNN 可以表示子图的语义信息，将网络中一小部分节点构成的语义表示出来，这是以前 Graph Embedding 不容易做到的。GNN 还可以在整个图网络上进行信息传播、聚合等建模，也就是说它可以把图网络当成一个整体进行建模。此外，GNN 对单个节点的表示也可以做得更好，因为它可以更好地建模周围节点丰富信息。

在传统图建模中，随机游走、最短路径等图方法会利用符号知识，但这些方法并没有办法很好地利用每个节点的语义信息。而深度学习技术更擅长处理非结构文本、图像等数据。简言之，我们可以将 GNN 看做将深度学习技术应用到符号表示的图数据上，或者说是从非结构化数据扩展到了结构化数据。GNN 能够充分融合符号表示和低维向量表示，发挥两者优势。

图建模论文与代码

在 的一项开源工作中，开发者收集了图建模相关的论文与实现，并且从经典的 Graph Embedding、Graph Kernel 到图神经网络都有涉及。它们在图嵌入、图分类、图表征等领域都是非常重要的论文。

项目地址：benedekrozemberczki/awesome-graph-classification

该项目主要收集的论文领域如下所示：

1. Factorization

2. Spectral and Statistical Fingerprints

3. Graph Neural Network

4. Graph Kernels

因式分解法

· Learning Graph Representation via Frequent Subgraphs (SDM 2018)

· Dang Nguyen Wei Luo Tu Dinh Nguyen Svetha Venkatesh Dinh Phung

· Paper：https://epubs.siam.org/doi/10.1137/1.9781611975321.35

· Python：nphdang/GE-FSG

· Anonymous Walk Embeddings (ICML 2018)

· Sergey Ivanov and Evgeny Burnaev

· Paper：https://arxiv.org/pdf/1805.11921.pdf

· Python：nd7141/AWE

· Graph2vec (MLGWorkshop 2017)

· Annamalai Narayanan Mahinthan Chandramohan Lihui Chen Yang Liu and Santhoshkumar Saminathan

· Paper：https://arxiv.org/abs/1707.05005

· Python High Performance：benedekrozemberczki/graph2vec

· Python Reference：MLDroid/graph2vec_tf

· Subgraph2vec (MLGWorkshop 2016)

· Annamalai Narayanan Mahinthan Chandramohan Lihui Chen Yang Liu and Santhoshkumar Saminathan

· Paper：https://arxiv.org/abs/1606.08928

· Python High Performance：MLDroid/subgraph2vec_gensim

· Python Reference：MLDroid/subgraph2vec_tf

· Rdf2Vec: RDF Graph Embeddings for Data Mining (ISWC 2016)

· Petar Ristoski and Heiko Paulheim

· Paper：https://link.springer.com/chapter/10.1007/978-3-319-46523-4_30

· Python Reference：airobert/RDF2VecAtWebScale

· Deep Graph Kernels (KDD 2015)

· Pinar Yanardag and S.V.N. Vishwanathan

· Paper：https://dl.acm.org/citation.cfm?id=2783417

· Python Reference：pankajk/Deep-Graph-Kernels

Spectral and Statistical Fingerprints

· A Simple Yet Effective Baseline for Non-Attribute Graph Classification (ICLR RLPM 2019)

· Chen Cai Yusu Wang

· Paper：https://arxiv.org/abs/1811.03508

· Python Reference：Chen-Cai-OSU/LDP

· NetLSD (KDD 2018)

· Anton Tsitsulin Davide Mottin Panagiotis Karras Alex Bronstein and Emmanuel Müller

· Paper：https://arxiv.org/abs/1805.10712

· Python Reference：xgfs/NetLSD

· A Simple Baseline Algorithm for Graph Classification (Relational Representation Learning NIPS 2018)

· Nathan de Lara and Edouard Pineau

· Paper：https://arxiv.org/pdf/1810.09155.pdf

· Python Reference：edouardpineau/A-simple-baseline-algorithm-for-graph-classification

· Multi-Graph Multi-Label Learning Based on Entropy (Entropy NIPS 2018)

· Zixuan Zhu and Yuhai Zhao

· Paper：https:// .com/TonyZZX/MultiGraph_MultiLabel_Learning/blob/master/entropy-20-00245.pdf

· Python Reference：TonyZZX/MultiGraph_MultiLabel_Learning

· Hunt For The Unique Stable Sparse And Fast Feature Learning On Graphs (NIPS 2017)

· Saurabh Verma and Zhi-Li Zhang

· Paper：https://papers.nips.cc/paper/6614-hunt-for-the-unique-stable-sparse-and-fast-feature-learning-on-graphs.pdf

· Python Reference：https:// .com/vermaMachineLearning/FGSD

· Joint Structure Feature Exploration and Regularization for Multi-Task Graph Classification (TKDE 2015)

· Shirui Pan Jia Wu Xingquan Zhuy Chengqi Zhang and Philip S. Yuz

· Paper：https://ieeexplore.ieee.org/document/7302040

· Java Reference：https:// .com/shiruipan/MTG

· NetSimile: A Scalable Approach to Size-Independent Network Similarity (arXiv 2012)

· Michele Berlingerio Danai Koutra Tina Eliassi-Rad and Christos Faloutsos

· Paper：https://arxiv.org/abs/1209.2684

· Python：https:// .com/kristyspatel/Netsimile

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