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2018 | OriginalPaper | Chapter

Kernel Graph Convolutional Neural Networks

Authors : Giannis Nikolentzos, Polykarpos Meladianos, Antoine Jean-Pierre Tixier, Konstantinos Skianis, Michalis Vazirgiannis

Published in: Artificial Neural Networks and Machine Learning – ICANN 2018

Publisher: Springer International Publishing

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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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Footnotes
1
The datasets, further references and statistics are available at https://​ls11-www.​cs.​tu-dortmund.​de/​staff/​morris/​graphkerneldatas​ets.
 
Literature
1.
go back to reference Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. JSTAT 2008(10), 1–12 (2008)CrossRef Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. JSTAT 2008(10), 1–12 (2008)CrossRef
2.
go back to reference Borgwardt, K.M., Kriegel, H.: Shortest-path kernels on graphs. In: ICDM, pp. 74–81 (2005) Borgwardt, K.M., Kriegel, H.: Shortest-path kernels on graphs. In: ICDM, pp. 74–81 (2005)
3.
go back to reference Bruna, J., Zaremba, W., Szlam, A., LeCun, Y.: Spectral networks and locally connected networks on graphs. In: ICLR (2014) Bruna, J., Zaremba, W., Szlam, A., LeCun, Y.: Spectral networks and locally connected networks on graphs. In: ICLR (2014)
4.
go back to reference Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: NIPS, pp. 3837–3845 (2016) Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: NIPS, pp. 3837–3845 (2016)
6.
go back to reference Horváth, T., Gärtner, T., Wrobel, S.: Cyclic Pattern Kernels for Predictive Graph Mining. In: KDD, pp. 158–167 (2004) Horváth, T., Gärtner, T., Wrobel, S.: Cyclic Pattern Kernels for Predictive Graph Mining. In: KDD, pp. 158–167 (2004)
7.
go back to reference Johansson, F., Jethava, V., Dubhashi, D., Bhattacharyya, C.: Global graph kernels using geometric embeddings. In: ICML, pp. 694–702 (2014) Johansson, F., Jethava, V., Dubhashi, D., Bhattacharyya, C.: Global graph kernels using geometric embeddings. In: ICML, pp. 694–702 (2014)
8.
go back to reference Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: ICLR (2017) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: ICLR (2017)
9.
go back to reference Kondor, R., Pan, H.: The multiscale laplacian graph kernel. In: NIPS, pp. 2982–2990 (2016) Kondor, R., Pan, H.: The multiscale laplacian graph kernel. In: NIPS, pp. 2982–2990 (2016)
10.
go back to reference Niepert, M., Ahmed, M., Kutzkov, K.: Learning convolutional neural networks for graphs. In: ICML (2016) Niepert, M., Ahmed, M., Kutzkov, K.: Learning convolutional neural networks for graphs. In: ICML (2016)
11.
go back to reference Nikolentzos, G., Meladianos, P., Vazirgiannis, M.: Matching node embeddings for graph similarity. In: AAAI, pp. 2429–2435 (2017) Nikolentzos, G., Meladianos, P., Vazirgiannis, M.: Matching node embeddings for graph similarity. In: AAAI, pp. 2429–2435 (2017)
12.
go back to reference Shervashidze, N., Schweitzer, P., Van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-Lehman graph kernels. JMLR 12, 2539–2561 (2011)MathSciNetMATH Shervashidze, N., Schweitzer, P., Van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-Lehman graph kernels. JMLR 12, 2539–2561 (2011)MathSciNetMATH
13.
go back to reference Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: AISTATS, pp. 488–495 (2009) Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: AISTATS, pp. 488–495 (2009)
14.
go back to reference Tixier, A., Nikolentzos, G., Meladianos, P., Vazirgiannis, M.: Classifying graphs as images with convolutional neural networks. arXiv:1708.02218 (2017) Tixier, A., Nikolentzos, G., Meladianos, P., Vazirgiannis, M.: Classifying graphs as images with convolutional neural networks. arXiv:​1708.​02218 (2017)
15.
go back to reference Vialatte, J.C., Gripon, V., Mercier, G.: Generalizing the convolution operator to extend CNNs to irregular domains. arXiv preprint arXiv:1606.01166 (2016) Vialatte, J.C., Gripon, V., Mercier, G.: Generalizing the convolution operator to extend CNNs to irregular domains. arXiv preprint arXiv:​1606.​01166 (2016)
16.
go back to reference Vishwanathan, S.V.N., Schraudolph, N.N., Kondor, R., Borgwardt, K.M.: Graph kernels. JMLR 11, 1201–1242 (2010)MathSciNetMATH Vishwanathan, S.V.N., Schraudolph, N.N., Kondor, R., Borgwardt, K.M.: Graph kernels. JMLR 11, 1201–1242 (2010)MathSciNetMATH
17.
go back to reference Williams, C.K., Seeger, M.: Using the Nyström method to speed up kernel machines. In: NIPS, pp. 661–667 (2000) Williams, C.K., Seeger, M.: Using the Nyström method to speed up kernel machines. In: NIPS, pp. 661–667 (2000)
18.
go back to reference Yanardag, P., Vishwanathan, S.: A structural smoothing framework for robust graph comparison. In: NIPS, pp. 2125–2133 (2015) Yanardag, P., Vishwanathan, S.: A structural smoothing framework for robust graph comparison. In: NIPS, pp. 2125–2133 (2015)
19.
go back to reference Yanardag, P., Vishwanathan, S.: Deep graph kernels. In: KDD, pp. 1365–1374 (2015) Yanardag, P., Vishwanathan, S.: Deep graph kernels. In: KDD, pp. 1365–1374 (2015)
20.
go back to reference Zhang, Y., Liang, P., Wainwright, M.J.: Convexified convolutional neural networks. In: ICML, pp. 4044–4053 (2017) Zhang, Y., Liang, P., Wainwright, M.J.: Convexified convolutional neural networks. In: ICML, pp. 4044–4053 (2017)
Metadata
Title
Kernel Graph Convolutional Neural Networks
Authors
Giannis Nikolentzos
Polykarpos Meladianos
Antoine Jean-Pierre Tixier
Konstantinos Skianis
Michalis Vazirgiannis
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-030-01418-6_3

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