{"type":"ScholarlyArticle","title":"Filtration-Enhanced Graph Transformation","authors":[{"name":"Zijian Chen","slug":"zijian-chen","given":"Zijian","family":"Chen","affiliation":"Beijing Institute of Technology"},{"name":"Rong-Hua Li","slug":"rong-hua-li","given":"Rong-Hua","family":"Li","affiliation":"Beijing Institute of Technology"},{"name":"Hongchao Qin","slug":"hongchao-qin","given":"Hongchao","family":"Qin","affiliation":"Beijing Institute of Technology"},{"name":"Huanzhong Duan","slug":"huanzhong-duan","given":"Huanzhong","family":"Duan","affiliation":"Tencent"},{"name":"Yanxiong Lu","slug":"yanxiong-lu","given":"Yanxiong","family":"Lu","affiliation":"Tencent"},{"name":"Qiangqiang Dai","slug":"qiangqiang-dai","given":"Qiangqiang","family":"Dai","affiliation":"Beijing Institute of Technology"},{"name":"Guoren Wang","slug":"guoren-wang","given":"Guoren","family":"Wang","affiliation":"Beijing Institute of Technology"}],"abstract":"Graph kernels and graph neural networks (GNNs) are widely used for the classification of graph data. However, many existing graph kernels and GNNs have limited expressive power, because they cannot distinguish graphs if the classic 1-dimensional Weisfeiler-Leman (1-WL) algorithm does not distinguish them. To break the 1-WL expressiveness barrier, we propose a novel method called filtration-enhanced graph transformation, which is based on a concept from the area of topological data analysis. In a nutshell, our approach first transforms each original graph into a filtration-enhanced graph based on a certain pre-defined filtration operation, and then uses the transformed graphs as the inputs for graph kernels or GNNs. The striking feature of our approach is that it is a plug-in method and can be applied in any graph kernel and GNN to enhance their expressive power. We theoretically and experimentally demonstrate that our solutions exhibit significantly better performance than the state-of-the art solutions for graph classification tasks.","doi":"10.24963/ijcai.2022/276","url":"https://ijcai.org/proceedings/2022/276","pdf":"https://ijcai.org/proceedings/2022/0276.pdf","markdown":"https://ijcai.org/proceedings/2022/276.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/276","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Data Mining","track":"Main Track","number":276,"pages":{"first":1987,"last":1993},"keywords":["Machine Learning: Sequence and Graph Learning","Data Mining: Mining Graphs"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986795","length_sec":88,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984938","length_sec":312,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Abboud et al., 2021] Ralph Abboud, İsmail İlkan Ceylan, Martin Grohe, and Thomas Lukasiewicz. The surprising power of graph neural networks with random node initialization. In IJCAI, 2021.","title":"The surprising power of graph neural networks with random node initialization","authors":"Ralph Abboud, Martin İsmail İlkan Ceylan, Thomas Grohe, Lukasiewicz","year":"2021","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2021/291"},{"position":2,"raw":"[Borgwardt and Kriegel, 2005] Karsten M. Borgwardt and Hans- Peter Kriegel. Shortest-path kernels on graphs. In ICDM, 2005.","title":"Shortest-path kernels on graphs","authors":"Karsten M Borgwardt, Hans-Peter Kriegel","year":"2005","venue":"ICDM","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bouritsas et al., 2020] Giorgos Bouritsas, Fabrizio Frasca, Ste- fanos Zafeiriou, and Michael M. Bronstein. Improving graph neural network expressivity via subgraph isomorphism counting. CoRR, abs/2006.09252, 2020.","title":"Improving graph neural network expressivity via subgraph isomorphism counting","authors":"Giorgos Bouritsas, Fabrizio Frasca, Stefanos Zafeiriou, Michael M Bronstein","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chiba and Nishizeki, 1985] Norishige Chiba and Takao Nishizeki. Arboricity and subgraph listing algorithms. SIAM Journal on computing, 14(1):210-223, 1985.","title":"Norishige Chiba and Takao Nishizeki. Arboricity and subgraph listing algorithms","authors":"Nishizeki Chiba","year":"1985","venue":"SIAM Journal on computing","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Du et al., 2019] Simon S. Du, Kangcheng Hou, Ruslan Salakhut- dinov, Barnabás Póczos, Ruosong Wang, and Keyulu Xu. Graph neural tangent kernel: Fusing graph neural networks with graph kernels. In NeurIPS, 2019.","title":"Graph neural tangent kernel: Fusing graph neural networks with graph kernels","authors":"Simon S Du, Kangcheng Hou, Ruslan Salakhutdinov, Barnabás Póczos, Ruosong Wang, Keyulu Xu","year":"2019","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Edelsbrunner et al., 2002] Herbert Edelsbrunner, David Letscher, and Afra Zomorodian. Topological persistence and simplifica- tion. Discret. Comput. Geom., 28(4):511-533, 2002.","title":"Topological persistence and simplification","authors":"Herbert Edelsbrunner, David Letscher, Afra Zomorodian","year":"2002","venue":"Discret. Comput. Geom","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Errica et al., 2020] Federico Errica, Marco Podda, Davide Bacciu, and Alessio Micheli. A fair comparison of graph neural networks for graph classification. In ICLR, 2020.","title":"A fair comparison of graph neural networks for graph classification","authors":"Federico Errica, Marco Podda, Davide Bacciu, Alessio Micheli","year":"2020","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hamilton et al., 2017] William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In NIPS, 2017.","title":"Inductive representation learning on large graphs","authors":"William L Hamilton, Zhitao Ying, Jure Leskovec","year":"2017","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Hofer et al., 2020] Christoph D. Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, and Roland Kwitt. Graph filtration learning. In ICML, 2020.","title":"Graph filtration learning","authors":"Christoph D Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, Roland Kwitt","year":"2020","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Horváth et al., 2004] Tamás Horváth, Thomas Gärtner, and Stefan Wrobel. Cyclic pattern kernels for predictive graph mining. In KDD, 2004.","title":"Cyclic pattern kernels for predictive graph mining","authors":"Tamás Horváth, Thomas Gärtner, Stefan Wrobel","year":"2004","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Kondor and Pan, 2016] Risi Kondor and Horace Pan. The multi- scale laplacian graph kernel. In NIPS, 2016.","title":"The multiscale laplacian graph kernel","authors":"Risi Kondor, Horace Pan","year":"2016","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Kriege and Mutzel, 2012] Nils M. Kriege and Petra Mutzel. Sub- graph matching kernels for attributed graphs. In ICML, 2012.","title":"Subgraph matching kernels for attributed graphs","authors":"Nils M Kriege, Petra Mutzel","year":"2012","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Kriege et al., 2016] Nils M. Kriege, Pierre-Louis Giscard, and Richard C. Wilson. On valid optimal assignment kernels and applications to graph classification. In NIPS, 2016.","title":"On valid optimal assignment kernels and applications to graph classification","authors":"Nils M Kriege, Pierre-Louis Giscard, Richard C Wilson","year":"2016","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kriege et al., 2020] Nils M Kriege, Fredrik D Johansson, and Christopher Morris. A survey on graph kernels. Applied Net- work Science, 5(1):1-42, 2020.","title":"A survey on graph kernels","authors":"Nils M Kriege, Christopher Fredrik D Johansson, Morris","year":"2020","venue":"Applied Network Science","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lee et al., 2019] Junhyun Lee, Inyeop Lee, and Jaewoo Kang. Self-attention graph pooling. In ICML, 2019.","title":"Self-attention graph pooling","authors":"Lee","year":"2019","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lin et al., 2011] Yong Lin, Linyuan Lu, and Shing-Tung Yau. Ricci curvature of graphs. Tohoku Mathematical Journal, Sec- ond Series, 63(4):605-627, 2011.","title":"Ricci curvature of graphs","authors":"Yong Lin, Linyuan Lu, Shing-Tung Yau","year":"2011","venue":"Tohoku Mathematical Journal, Second Series","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Matula and Beck, 1983] David W. Matula and Leland L. Beck. Smallest-last ordering and clustering and graph coloring algo- rithms. J. ACM, 30(3):417-427, 1983.","title":"Smallest-last ordering and clustering and graph coloring algorithms","authors":"David W Matula, Leland L Beck","year":"1983","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Morris et al., 2017] Christopher Morris, Kristian Kersting, and Pe- tra Mutzel. Glocalized weisfeiler-lehman graph kernels: Global- local feature maps of graphs. In ICDM, 2017.","title":"Glocalized weisfeiler-lehman graph kernels: Globallocal feature maps of graphs","authors":"Christopher Morris, Kristian Kersting, Petra Mutzel","year":"2017","venue":"ICDM","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Morris et al., 2020] Christopher Morris, Gaurav Rattan, and Pe- tra Mutzel. Weisfeiler and leman go sparse: Towards scalable higher-order graph embeddings. In NeurIPS, 2020.","title":"Weisfeiler and leman go sparse: Towards scalable higher-order graph embeddings","authors":"Christopher Morris, Gaurav Rattan, Petra Mutzel","year":"2020","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Nikolentzos et al., 2017a] Giannis Nikolentzos, Polykarpos Mela- dianos, Franc ¸ois Rousseau, Yannis Stavrakas, and Michalis Vazirgiannis. Shortest-path graph kernels for document similar- ity. In EMNLP, 2017.","title":"Shortest-path graph kernels for document similarity","authors":"Nikolentzos","year":"2017","venue":"EMNLP","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Nikolentzos et al., 2017b] Giannis Nikolentzos, Polykarpos Mela- dianos, and Michalis Vazirgiannis. Matching node embeddings for graph similarity. In AAAI, 2017.","title":"Giannis Nikolentzos, Polykarpos Meladianos, and Michalis Vazirgiannis. Matching node embeddings for graph similarity","authors":"Nikolentzos","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[O'Bray et al., 2021] Leslie O'Bray, Bastian Rieck, and Karsten Borgwardt. Filtration curves for graph representation. In KDD, 2021.","title":"Filtration curves for graph representation","authors":"O' Leslie, Bastian Bray, Karsten Rieck, Borgwardt","year":"2021","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Sato et al., 2021] Ryoma Sato, Makoto Yamada, and Hisashi Kashima. Random features strengthen graph neural networks. In SDM, 2021.","title":"Random features strengthen graph neural networks","authors":"Ryoma Sato, Makoto Yamada, Hisashi Kashima","year":"2021","venue":"SDM","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Seidman, 1983] Stephen B Seidman. Network structure and mini- mum degree. Social networks, 5(3):269-287, 1983.","title":"Network structure and minimum degree","authors":"Stephen B Seidman","year":"1983","venue":"Social networks","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Shervashidze et al., 2009] Nino Shervashidze, S. V. N. Vish- wanathan, Tobias Petri, Kurt Mehlhorn, and Karsten M. Borg- wardt. Efficient graphlet kernels for large graph comparison. In AISTATS, 2009.","title":"Efficient graphlet kernels for large graph comparison","authors":"S V N Nino Shervashidze, Tobias Vishwanathan, Kurt Petri, Karsten M Mehlhorn, Borgwardt","year":"2009","venue":"AISTATS","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Shervashidze et al., 2011] Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, and Karsten M. Borg- wardt. Weisfeiler-lehman graph kernels. J. Mach. Learn. Res., 12:2539-2561, 2011.","title":"Borgwardt. Weisfeiler-lehman graph kernels","authors":"Nino Shervashidze, Pascal Schweitzer, Erik Jan Van Leeuwen, Kurt Mehlhorn, Karsten M","year":"2011","venue":"J. Mach. Learn. Res","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Siglidis et al., 2020] Giannis Siglidis, Giannis Nikolentzos, Stratis Limnios, Christos Giatsidis, Konstantinos Skianis, and Michalis Vazirgiannis. Grakel: A graph kernel library in python. Journal of Machine Learning Research, 21(54):1-5, 2020.","title":"Grakel: A graph kernel library in python","authors":"Giannis Siglidis, Giannis Nikolentzos, Stratis Limnios, Christos Giatsidis, Konstantinos Skianis, Michalis Vazirgiannis","year":"2020","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Weisfeiler and Leman, 1968] Boris Weisfeiler and A. A. Leman. A reduction of a graph to a canonical form and an algebra aris- ing during this reduction. Nauchno-Technicheskaya Informat- siya, 2(9):12-16, 1968.","title":"A reduction of a graph to a canonical form and an algebra arising during this reduction","authors":"Boris Weisfeiler, A A Leman","year":"1968","venue":"Nauchno-Technicheskaya Informatsiya","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Wijesinghe and Wang, 2022] Asiri Wijesinghe and Qing Wang. A new perspective on \"how graph neural networks go beyond weisfeiler-lehman?\". In International Conference on Learning Representations, 2022.","title":"A new perspective on \"how graph neural networks go beyond weisfeiler-lehman?","authors":"Asiri Wijesinghe, Qing Wang","year":"2022","venue":"International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Xu et al., 2019] Keyulu Xu, Weihua Hu, Jure Leskovec, and Ste- fanie Jegelka. How powerful are graph neural networks? In ICLR, 2019.","title":"How powerful are graph neural networks?","authors":"Keyulu Xu, Weihua Hu, Jure Leskovec, Stefanie Jegelka","year":"2019","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Yanardag and Vishwanathan, 2015] Pinar Yanardag and S. V. N. Vishwanathan. Deep graph kernels. In KDD, 2015.","title":"Deep graph kernels","authors":"Pinar Yanardag, S V N Vishwanathan","year":"2015","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[You et al., 2021] Jiaxuan You, Jonathan M. Gomes-Selman, Rex Ying, and Jure Leskovec. Identity-aware graph neural networks. In AAAI, 2021.","title":"Identity-aware graph neural networks","authors":"Jiaxuan You, Jonathan M Gomes-Selman, Rex Ying, Jure Leskovec","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Zhang et al., 2018] Zhen Zhang, Mianzhi Wang, Yijian Xiang, Yan Huang, and Arye Nehorai. Retgk: Graph kernels based on return probabilities of random walks. In NeurIPS, 2018.","title":"Retgk: Graph kernels based on return probabilities of random walks","authors":"Zhen Zhang, Mianzhi Wang, Yijian Xiang, Yan Huang, Arye Nehorai","year":"2018","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Zhao and Wang, 2019] Qi Zhao and Yusu Wang. Learning met- rics for persistence-based summaries and applications for graph classification. In NeurIPS, 2019.","title":"Learning metrics for persistence-based summaries and applications for graph classification","authors":"Wang ; ] Qi Zhao, Yusu Zhao, Wang","year":"2019","venue":"NeurIPS","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}