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Kernel Graph Convolutional Neural Networks

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Artificial Neural Networks and Machine Learning – ICANN 2018 (ICANN 2018)

Abstract

Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage approach decouples data representation from learning, which is suboptimal. On the other hand, Convolutional Neural Networks (CNNs) have the capability to learn their own features directly from the raw data during training. Unfortunately, they cannot handle irregular data such as graphs. We address this challenge by using graph kernels to embed meaningful local neighborhoods of the graphs in a continuous vector space. A set of filters is then convolved with these patches, pooled, and the output is then passed to a feedforward network. With limited parameter tuning, our approach outperforms strong baselines on 7 out of 10 benchmark datasets. Code and data are publicly available (https://github.com/giannisnik/cnn-graph-classification).

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Notes

  1. 1.

    The datasets, further references and statistics are available at https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets.

References

  1. Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. JSTAT 2008(10), 1–12 (2008)

    Article  Google Scholar 

  2. Borgwardt, K.M., Kriegel, H.: Shortest-path kernels on graphs. In: ICDM, pp. 74–81 (2005)

    Google Scholar 

  3. Bruna, J., Zaremba, W., Szlam, A., LeCun, Y.: Spectral networks and locally connected networks on graphs. In: ICLR (2014)

    Google Scholar 

  4. Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: NIPS, pp. 3837–3845 (2016)

    Google Scholar 

  5. Fortunato, S., Hric, D.: Community detection in networks: a user guide. Phys. Rep. 659, 1–44 (2016)

    Article  MathSciNet  Google Scholar 

  6. Horváth, T., Gärtner, T., Wrobel, S.: Cyclic Pattern Kernels for Predictive Graph Mining. In: KDD, pp. 158–167 (2004)

    Google Scholar 

  7. Johansson, F., Jethava, V., Dubhashi, D., Bhattacharyya, C.: Global graph kernels using geometric embeddings. In: ICML, pp. 694–702 (2014)

    Google Scholar 

  8. Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: ICLR (2017)

    Google Scholar 

  9. Kondor, R., Pan, H.: The multiscale laplacian graph kernel. In: NIPS, pp. 2982–2990 (2016)

    Google Scholar 

  10. Niepert, M., Ahmed, M., Kutzkov, K.: Learning convolutional neural networks for graphs. In: ICML (2016)

    Google Scholar 

  11. Nikolentzos, G., Meladianos, P., Vazirgiannis, M.: Matching node embeddings for graph similarity. In: AAAI, pp. 2429–2435 (2017)

    Google Scholar 

  12. Shervashidze, N., Schweitzer, P., Van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-Lehman graph kernels. JMLR 12, 2539–2561 (2011)

    MathSciNet  MATH  Google Scholar 

  13. Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: AISTATS, pp. 488–495 (2009)

    Google Scholar 

  14. Tixier, A., Nikolentzos, G., Meladianos, P., Vazirgiannis, M.: Classifying graphs as images with convolutional neural networks. arXiv:1708.02218 (2017)

  15. Vialatte, J.C., Gripon, V., Mercier, G.: Generalizing the convolution operator to extend CNNs to irregular domains. arXiv preprint arXiv:1606.01166 (2016)

  16. Vishwanathan, S.V.N., Schraudolph, N.N., Kondor, R., Borgwardt, K.M.: Graph kernels. JMLR 11, 1201–1242 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Williams, C.K., Seeger, M.: Using the Nyström method to speed up kernel machines. In: NIPS, pp. 661–667 (2000)

    Google Scholar 

  18. Yanardag, P., Vishwanathan, S.: A structural smoothing framework for robust graph comparison. In: NIPS, pp. 2125–2133 (2015)

    Google Scholar 

  19. Yanardag, P., Vishwanathan, S.: Deep graph kernels. In: KDD, pp. 1365–1374 (2015)

    Google Scholar 

  20. Zhang, Y., Liang, P., Wainwright, M.J.: Convexified convolutional neural networks. In: ICML, pp. 4044–4053 (2017)

    Google Scholar 

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Correspondence to Giannis Nikolentzos .

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Nikolentzos, G., Meladianos, P., Tixier, A.JP., Skianis, K., Vazirgiannis, M. (2018). Kernel Graph Convolutional Neural Networks. In: Kůrková, V., Manolopoulos, Y., Hammer, B., Iliadis, L., Maglogiannis, I. (eds) Artificial Neural Networks and Machine Learning – ICANN 2018. ICANN 2018. Lecture Notes in Computer Science(), vol 11139. Springer, Cham. https://doi.org/10.1007/978-3-030-01418-6_3

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  • DOI: https://doi.org/10.1007/978-3-030-01418-6_3

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