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caotube,干货看这篇!想要了解图或图神经网络?没有比看论文更好的方式

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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。


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:


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:
  • Python:
  • Anonymous Walk Embeddings (ICML 2018)
  • Sergey Ivanov and Evgeny Burnaev
  • Paper:
  • Python:
  • Graph2vec (MLGWorkshop 2017)
  • Annamalai Narayanan, Mahinthan Chandramohan, Lihui Chen, Yang Liu, and Santhoshkumar Saminathan
  • Paper:
  • Python High Performance:
  • Python Reference:
  • Subgraph2vec (MLGWorkshop 2016)
  • Annamalai Narayanan, Mahinthan Chandramohan, Lihui Chen, Yang Liu, and Santhoshkumar Saminathan
  • Paper:
  • Python High Performance:
  • Python Reference:
  • Rdf2Vec: RDF Graph Embeddings for Data Mining (ISWC 2016)
  • Petar Ristoski and Heiko Paulheim
  • Paper:
  • Python Reference:
  • Deep Graph Kernels (KDD 2015)
  • Pinar Yanardag and S.V.N. Vishwanathan
  • Paper:
  • Python Reference:

Spectral and Statistical Fingerprints

  • A Simple Yet Effective Baseline for Non-Attribute Graph Classification (ICLR RLPM 2019)
  • Chen Cai, Yusu Wang
  • Paper:
  • Python Reference:
  • NetLSD (KDD 2018)
  • Anton Tsitsulin, Davide Mottin, Panagiotis Karras, Alex Bronstein, and Emmanuel Müller
  • Paper:
  • Python Reference:
  • A Simple Baseline Algorithm for Graph Classification (Relational Representation Learning, NIPS 2018)
  • Nathan de Lara and Edouard Pineau
  • Paper:
  • Python Reference:
  • Multi-Graph Multi-Label Learning Based on Entropy (Entropy NIPS 2018)
  • Zixuan Zhu and Yuhai Zhao
  • Paper:
  • Python Reference:
  • Hunt For The Unique, Stable, Sparse And Fast Feature Learning On Graphs (NIPS 2017)
  • Saurabh Verma and Zhi-Li Zhang
  • Paper:
  • Python Reference:
  • 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:
  • Java Reference:
  • NetSimile: A Scalable Approach to Size-Independent Network Similarity (arXiv 2012)
  • Michele Berlingerio, Danai Koutra, Tina Eliassi-Rad, and Christos Faloutsos
  • Paper:
  • Python:

图神经网络

  • Self-Attention Graph Pooling (ICML 2019)
  • Junhyun Lee, Inyeop Lee, Jaewoo Kang
  • Paper:
  • Python Reference:
  • Variational Recurrent Neural Networks for Graph Classification (ICLR 2019)
  • Edouard Pineau, Nathan de Lara
  • Paper:
  • Python Reference:
  • Crystal Graph Neural Networks for Data Mining in Materials Science (Arxiv 2019)
  • Takenori Yamamoto
  • Paper:
  • Python Reference:
  • Explainability Techniques for Graph Convolutional Networks (ICML 2019)
  • Federico Baldassarre, Hossein Azizpour
  • Paper:
  • Python Reference:
  • Semi-Supervised Graph Classification: A Hierarchical Graph Perspective (WWW 2019)
  • Jia Li, Yu Rong, Hong Cheng, Helen Meng, Wenbing Huang, and Junzhou Huang
  • Paper:
  • Python Reference:
  • Capsule Graph Neural Network (ICLR 2019)
  • Zhang Xinyi and Lihui Chen
  • Paper:
  • Python Reference:
  • How Powerful are Graph Neural Networks? (ICLR 2019)
  • Keyulu Xu, Weihua Hu, Jure Leskovec, Stefanie Jegelka
  • Paper:
  • Python Reference:
  • 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:
  • Python Reference:
  • Capsule Neural Networks for Graph Classification using Explicit Tensorial Graph Representations (Arxiv 2019)
  • Marcelo Daniel Gutierrez Mallea, Peter Meltzer, and Peter J Bentley
  • Paper:
  • Python Reference:
  • Three-Dimensionally Embedded Graph Convolutional Network for Molecule Interpretation (Arxiv 2018)
  • Hyeoncheol Cho and Insung. S. Choi
  • Paper:
  • Python Reference:
  • Learning Graph-Level Representations with Recurrent Neural Networks (Arxiv 2018)
  • Yu Jin and Joseph F. JaJa
  • Paper:
  • Python Reference:
  • Graph Capsule Convolutional Neural Networks (ICML 2018)
  • Saurabh Verma and Zhi-Li Zhang
  • Paper:
  • Python Reference:
  • Graph Classification Using Structural Attention (KDD 2018)
  • John Boaz Lee, Ryan Rossi, and Xiangnan Kong
  • Paper:
  • Python Pytorch Reference:
  • Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation (NIPS 2018)
  • Jiaxuan You, Bowen Liu, Rex Ying, Vijay Pande, and Jure Leskovec
  • Paper:
  • Python Reference:
  • Hierarchical Graph Representation Learning with Differentiable Pooling (NIPS 2018)
  • Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton and Jure Leskovec
  • Paper:
  • Python Reference:
  • Contextual Graph Markov Model: A Deep and Generative Approach to Graph Processing (ICML 2018)
  • Davide Bacciu, Federico Errica, and Alessio Micheli
  • Paper:
  • Python Reference:
  • MolGAN: An Implicit Generative Model for Small Molecular Graphs (ICML 2018)
  • Nicola De Cao and Thomas Kipf
  • Paper:
  • Python Reference:
  • Deeply Learning Molecular Structure-Property Relationships Using Graph Attention Neural Network (2018)
  • Seongok Ryu, Jaechang Lim, and Woo Youn Kim
  • Paper:
  • Python Reference:
  • 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:
  • Python Reference:
  • Python Reference:
  • Python Alternative:
  • Learning Graph Distances with Message Passing Neural Networks (ICPR 2018)
  • Pau Riba, Andreas Fischer, Josep Llados, and Alicia Fornes
  • Paper:
  • Python Reference:
  • 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:
  • Python Reference:
  • 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:
  • Python Reference:
  • Residual Gated Graph ConvNets (ICLR 2018)
  • Xavier Bresson and Thomas Laurent
  • Paper:
  • Python Pytorch Reference:
  • An End-to-End Deep Learning Architecture for Graph Classification (AAAI 2018)
  • Muhan Zhang, Zhicheng Cui, Marion Neumann and Yixin Chen
  • Paper:
  • Python Tensorflow Reference:
  • Python Pytorch Reference:
  • MATLAB Reference:
  • Python Alternative:
  • Python Alternative:
  • SGR: Self-Supervised Spectral Graph Representation Learning (KDD DLDay 2018)
  • Anton Tsitsulin, Davide Mottin, Panagiotis Karra, Alex Bronstein and Emmanueal Müller
  • Paper:
  • Python Reference:
  • Deep Learning with Topological Signatures (NIPS 2017)
  • Christoph Hofer, Roland Kwitt, Marc Niethammer, and Andreas Uhl
  • paper:
  • Python Reference:
  • Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (CVPR 2017)
  • Martin Simonovsky and Nikos Komodakis
  • paper:
  • Python Reference:
  • Deriving Neural Architectures from Sequence and Graph Kernels (ICML 2017)
  • Tao Lei, Wengong Jin, Regina Barzilay, and Tommi Jaakkola
  • Paper:
  • Python Reference:
  • Protein Interface Prediction using Graph Convolutional Networks (NIPS 2017)
  • Alex Fout, Jonathon Byrd, Basir Shariat and Asa Ben-Hur
  • Paper:
  • Python Reference:
  • Graph Classification with 2D Convolutional Neural Networks (2017)
  • Antoine J.-P. Tixier, Giannis Nikolentzos, Polykarpos Meladianos and Michalis Vazirgiannis
  • Paper:
  • Python Reference:
  • CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters (IEEE TSP 2017)
  • Ron Levie, Federico Monti, Xavier Bresson, Michael M. Bronstein
  • Paper:
  • Python Reference:
  • Semi-supervised Learning of Hierarchical Representations of Molecules Using Neural Message Passing (2017)
  • Hai Nguyen, Shin-ichi Maeda, Kenta Oono
  • Paper:
  • Python Reference:
  • Kernel Graph Convolutional Neural Networks (2017)
  • Giannis Nikolentzos, Polykarpos Meladianos, Antoine Jean-Pierre Tixier, Konstantinos Skianis, Michalis Vazirgiannis
  • Paper:
  • Python Reference:
  • 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:
  • Python Reference:
  • Learning Convolutional Neural Networks for Graphs (ICML 2016)
  • Mathias Niepert, Mohamed Ahmed, Konstantin Kutzkov
  • Paper:
  • Python Reference:
  • Gated Graph Sequence Neural Networks (ICLR 2016)
  • Yujia Li, Daniel Tarlow, Marc Brockschmidt, Richard Zemel
  • Paper:
  • Python TensorFlow:
  • Python PyTorch:
  • Python Reference:
  • 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:
  • Python Reference:
  • Python Reference:
  • Python Reference:
  • Python Reference:

Graph Kernels

  • Message Passing Graph Kernels (2018)
  • Giannis Nikolentzos, Michalis Vazirgiannis
  • Paper:
  • Python Reference:
  • Matching Node Embeddings for Graph Similarity (AAAI 2017)
  • Giannis Nikolentzos, Polykarpos Meladianos, and Michalis Vazirgiannis
  • Paper:
  • Global Weisfeiler-Lehman Graph Kernels (2017)
  • Christopher Morris, Kristian Kersting and Petra Mutzel
  • Paper:
  • C++ Reference:
  • On Valid Optimal Assignment Kernels and Applications to Graph Classification (2016)
  • Nils Kriege, Pierre-Louis Giscard, Richard Wilson
  • Paper:
  • Java Reference:
  • Efficient Comparison of Massive Graphs Through The Use Of ‘Graph Fingerprints’ (MLGWorkshop 2016)
  • Stephen Bonner, John Brennan, and A. Stephen McGough
  • Paper:
  • python Reference:
  • The Multiscale Laplacian Graph Kernel (NIPS 2016)
  • Risi Kondor and Horace Pan
  • Paper:
  • C++ Reference:
  • Faster Kernels for Graphs with Continuous Attributes (ICDM 2016)
  • Christopher Morris, Nils M. Kriege, Kristian Kersting and Petra Mutzel
  • Paper:
  • Python Reference:
  • Propagation Kernels: Efficient Graph Kernels From Propagated Information (Machine Learning 2016)
  • Neumann, Marion and Garnett, Roman and Bauckhage, Christian and Kersting, Kristian
  • Paper:
  • Matlab Reference:
  • Halting Random Walk Kernels (NIPS 2015)
  • Mahito Sugiyama and Karsten M. Borgward
  • Paper:
  • C++ Reference:
  • Scalable Kernels for Graphs with Continuous Attributes (NIPS 2013)
  • Aasa Feragen, Niklas Kasenburg, Jens Petersen, Marleen de Bruijne and Karsten Borgwardt
  • Paper:
  • Subgraph Matching Kernels for Attributed Graphs (ICML 2012)
  • Nils Kriege and Petra Mutzel
  • Paper:
  • Python Reference:
  • Nested Subtree Hash Kernels for Large-Scale Graph Classification over Streams (ICDM 2012)
  • Bin Li, Xingquan Zhu, Lianhua Chi, Chengqi Zhang
  • Paper:
  • Python Reference:
  • Weisfeiler-Lehman Graph Kernels (JMLR 2011)
  • Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, and Karsten M. Borgwardt
  • Paper:
  • Python Reference:
  • Python Reference:
  • C++ Reference:
  • Fast Neighborhood Subgraph Pairwise Distance Kernel (ICML 2010)
  • Fabrizio Costa and Kurt De Grave
  • Paper:
  • C++ Reference:/blob/master/www.bioinf.uni-freiburg.de/~costa/EDeNcpp.tgz
  • Python Reference:
  • A Linear-time Graph Kernel (ICDM 2009)
  • Shohei Hido and Hisashi Kashima
  • Paper:
  • Python Reference:
  • Weisfeiler-Lehman Subtree Kernels (NIPS 2009)
  • Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, and Karsten M. Borgwardt
  • Paper:
  • Python Reference:
  • Python Reference:
  • C++ Reference:
  • Fast Computation of Graph Kernels (NIPS 2006)
  • S. V. N. Vishwanathan, Karsten M. Borgwardt, and Nicol N. Schraudolph
  • Paper:
  • Python Reference:
  • C++ Reference:
  • Shortest-Path Kernels on Graphs (ICDM 2005)
  • Karsten M. Borgwardt and Hans-Peter Kriegel
  • Paper:
  • C++ Reference:
  • Cyclic Pattern Kernels For Predictive Graph Mining (KDD 2004)
  • Tamás Horváth, Thomas Gärtner, and Stefan Wrobel
  • Paper:;rep=rep1&type=pdf
  • Python Reference:
  • Extensions of Marginalized Graph Kernels (ICML 2004)
  • Pierre Mahe, Nobuhisa Ueda, Tatsuya Akutsu, Jean-Luc Perret, and Jean-Philippe Vert
  • Paper:
  • Python Reference:
  • Marginalized Kernels Between Labeled Graphs (ICML 2003)
  • Hisashi Kashima, Koji Tsuda, and Akihiro Inokuchi
  • Paper:
  • Python Reference:


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:

· Python:nphdang/GE-FSG

· Anonymous Walk Embeddings (ICML 2018)

· Sergey Ivanov and Evgeny Burnaev

· Paper:

· Python:nd7141/AWE

· Graph2vec (MLGWorkshop 2017)

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

· Paper:

· 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:

· 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:

· Python Reference:airobert/RDF2VecAtWebScale

· Deep Graph Kernels (KDD 2015)

· Pinar Yanardag and S.V.N. Vishwanathan

· Paper:

· 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:

· Python Reference:Chen-Cai-OSU/LDP

· NetLSD (KDD 2018)

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

· Paper:

· Python Reference:xgfs/NetLSD

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

· Nathan de Lara and Edouard Pineau

· Paper:

· 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

· 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:

· 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:

· 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:

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

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