想要了解圖或圖神經網路？沒有比看論文更好的方式

機器之心編輯

參與：思源

圖嵌入、圖表徵、圖分類、圖神經網路，這篇文章將介紹你需要的圖建模論文，當然它們都有配套實現的。

圖是一種非常神奇的表示方式，生活中絕大多數的現象或情境都能用圖來表示，例如人際關係網、道路交通網、信息互聯網等等。正如馬哲介紹事物具有普遍聯繫性，而圖正好能捕捉這種聯繫，所以用它來描述這個世界是再好不過的方法。

但圖這種結構化數據有個麻煩的地方，我們先要有圖才能進行後續的計算。但圖的搭建並不簡單，目前也沒有比較好的自動化方法，所以第一步還是需要挺多功夫的。只要各節點及邊都確定了，那麼圖就是一種非常強大且複雜的工具，模型也能推斷出圖中的各種隱藏知識。

不同時期的圖建模

其實，我們可以將圖建模分為圖神經網路與傳統的圖模型。其中以前的圖建模主要藉助 Graph Embedding 為不同的節點學習低維向量表徵，這借鑒了 NLP 中詞嵌入的思想。而圖神經網路藉助深度學習進行更強大的圖運算與圖表徵。

Graph Embedding 演算法聚焦在如何對網路節點進行低維向量表示，相似的節點在表徵空間中更加接近。相比之下，GNN 最大的優勢在於它不只可以對一個節點進行語義表示。

例如 GNN 可以表示子圖的語義信息，將網路中一小部分節點構成的語義表示出來，這是以前 Graph Embedding 不容易做到的。GNN 還可以在整個圖網路上進行信息傳播、聚合等建模，也就是說它可以把圖網路當成一個整體進行建模。此外，GNN 對單個節點的表示也可以做得更好，因為它可以更好地建模周圍節點豐富信息。

在傳統圖建模中，隨機遊走、最短路徑等圖方法會利用符號知識，但這些方法並沒有辦法很好地利用每個節點的語義信息。而深度學習技術更擅長處理非結構文本、圖像等數據。簡言之，我們可以將 GNN 看做將深度學習技術應用到符號表示的圖數據上，或者說是從非結構化數據擴展到了結構化數據。GNN 能夠充分融合符號表示和低維向量表示，發揮兩者優勢。

圖建模論文與代碼

在 GitHub 的一項開源工作中，開發者收集了圖建模相關的論文與實現，並且從經典的 Graph Embedding、Graph Kernel 到圖神經網路都有涉及。它們在圖嵌入、圖分類、圖表徵等領域都是非常重要的論文。

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

該項目主要收集的論文領域如下所示：

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

圖神經網路

• 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 G?rtner, 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

不同時期的圖建模

其實，我們可以將圖建模分為圖神經網路與傳統的圖模型。其中以前的圖建模主要藉助 Graph Embedding 為不同的節點學習低維向量表徵，這借鑒了 NLP 中詞嵌入的思想。而圖神經網路藉助深度學習進行更強大的圖運算與圖表徵。

Graph Embedding 演算法聚焦在如何對網路節點進行低維向量表示，相似的節點在表徵空間中更加接近。相比之下，GNN 最大的優勢在於它不只可以對一個節點進行語義表示。

例如 GNN 可以表示子圖的語義信息，將網路中一小部分節點構成的語義表示出來，這是以前 Graph Embedding 不容易做到的。GNN 還可以在整個圖網路上進行信息傳播、聚合等建模，也就是說它可以把圖網路當成一個整體進行建模。此外，GNN 對單個節點的表示也可以做得更好，因為它可以更好地建模周圍節點豐富信息。

在傳統圖建模中，隨機遊走、最短路徑等圖方法會利用符號知識，但這些方法並沒有辦法很好地利用每個節點的語義信息。而深度學習技術更擅長處理非結構文本、圖像等數據。簡言之，我們可以將 GNN 看做將深度學習技術應用到符號表示的圖數據上，或者說是從非結構化數據擴展到了結構化數據。GNN 能夠充分融合符號表示和低維向量表示，發揮兩者優勢。

圖建模論文與代碼

在 的一項開源工作中，開發者收集了圖建模相關的論文與實現，並且從經典的 Graph Embedding、Graph Kernel 到圖神經網路都有涉及。它們在圖嵌入、圖分類、圖表徵等領域都是非常重要的論文。

項目地址：benedekrozemberczki/awesome-graph-classification

該項目主要收集的論文領域如下所示：

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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