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A Persistent WeisfeilerLehman Procedure for Graph Classifjcation Bastian Rieck Christian Bock Karsten Borgwardt Graph classifjcation Graph Potential labels A Persistent WeisfeilerLehman Procedure for Graph Classifjcation Bastian Rieck,

  1. A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck Christian Bock Karsten Borgwardt

  2. Graph classifjcation Graph Potential labels A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  3. Graph classifjcation Neighbourhood aggregation A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  4. Our proposed method “P-WL = WL + TDA” A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  5. Topological features in graphs Connected components and cycles Graph A connected component Cycles A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019 1 2

  6. Finding topological features Calculating the persistent homology of a weighted graph Labelled graph A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  7. Finding topological features Calculating the persistent homology of a weighted graph Weisfeiler–Lehman aggregation A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  8. Finding topological features Calculating the persistent homology of a weighted graph Label multisets A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  9. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  10. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph Graph fjltration Topological feature descriptor A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  11. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph Graph fjltration Topological feature descriptor A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  12. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph Graph fjltration Topological feature descriptor A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  13. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph Graph fjltration Topological feature descriptor A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  14. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph Graph fjltration Topological feature descriptor A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  15. Finding topological features Calculating the persistent homology of a weighted graph Weighted graph Graph fjltration Topological feature descriptor A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

  16. Conclusion P-WL… …is almost as effjcient as the Weisfeiler–Lehman kernel …exhibits favourable performance …outperforms “deep” graph kernels …shows the potential of topological data analysis (TDA) Poster #224 A Persistent Weisfeiler–Lehman Procedure for Graph Classifjcation Bastian Rieck, Christian Bock, Karsten Borgwardt 11 June 2019

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