Abstract
Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the ordering of node neighbors, even when there is a geometric interpretation of the graph vertices that provides an order based on their spatial positions. To remedy this issue, we propose Spatial Graph Convolutional Network (SGCN) which uses spatial features to efficiently learn from graphs that can be naturally located in space. Our contribution is threefold: we propose a GCN-inspired architecture which (i) leverages node positions, (ii) is a proper generalization of both GCNs and Convolutional Neural Networks (CNNs), (iii) benefits from augmentation which further improves the performance and assures invariance with respect to the desired properties. Empirically, SGCN outperforms state-of-the-art graph-based methods on image classification and chemical tasks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
For all datasets, slight improvements can be observed with the augmented data.
References
Danel, T., et al.: Spatial graph convolutional networks. arXiv preprint arXiv:1909.05310 (2019)
Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in Neural Information Processing Systems, pp. 3844–3852 (2016)
Duvenaud, D.K., et al.: Convolutional networks on graphs for learning molecular fingerprints. In: Advances in Neural Information Processing Systems, pp. 2224–2232 (2015)
Fey, M., Lenssen, J.E., Weichert, F., Müller, H.: SplineCNN: fast geometric deep learning with continuous B-spline kernels. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 869–877 (2018)
Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., Dahl, G.E.: Neural message passing for quantum chemistry. In: Proceedings of the 34th International Conference on Machine Learning, vol. 70, pp. 1263–1272 (2017). JMLR.org
Kearnes, S., McCloskey, K., Berndl, M., Pande, V., Riley, P.: Molecular graph convolutions: moving beyond fingerprints. J. Comput. Aided Mol. Des. 30(8), 595–608 (2016). https://doi.org/10.1007/s10822-016-9938-8
Kim, Y.: Convolutional neural networks for sentence classification. arXiv preprint arXiv:1408.5882 (2014)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)
Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1097–1105 (2012)
Maziarka, Ł., Danel, T., Mucha, S., Rataj, K., Tabor, J., Jastrzębski, S.: Molecule-augmented attention transformer. In: Workshop on Graph Representation Learning, Neural Information Processing Systems 2019 (2019)
Monti, F., Boscaini, D., Masci, J., Rodola, E., Svoboda, J., Bronstein, M.M.: Geometric deep learning on graphs and manifolds using mixture model CNNs. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5115–5124 (2017)
Rogers, D., Hahn, M.: Extended-connectivity fingerprints. J. Chem. Inf. Model. 50(5), 742–754 (2010)
Seferbekov, S.S., Iglovikov, V., Buslaev, A., Shvets, A.: Feature pyramid network for multi-class land segmentation. In: CVPR Workshops, pp. 272–275 (2018)
Shang, C., et al.: Edge attention-based multi-relational graph convolutional networks. arXiv preprint arXiv:1802.04944 (2018)
Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. arXiv preprint arXiv:1710.10903 (2017)
Wu, Z., Ramsundar, B., Feinberg, E.N., Gomes, J., Geniesse, C., Pappu, A.S., Leswing, K., Pande, V.: Moleculenet: a benchmark for molecular machine learning. Chem. Sci. 9(2), 513–530 (2018)
Acknowledgements
The work of T. Danel was supported by the National Science Centre (Poland) grant no. 2018/31/B/ST6/00993. The work of P. Spurek was supported by the National Centre of Science (Poland) Grant No. 2019/33/B/ST6/00894. The work of J. Tabor was supported by the Foundation for Polish Science Grant No. POIR.04.04.00-00-14DE/18-00 co-financed by the European Union under the European Regional Development Fund. The work of M. Śmieja was supported by the grant no. LIDER/37/0137/L-9/17/NCBR/2018 from the Polish National Centre for Research and Development. The work of Ł. Struski was supported by the National Science Centre (Poland) grant no. 2017/25/B/ST6/01271. The work of Ł. Maziarka was supported by the National Science Centre (Poland) grant no. 2019/35/N/ST6/02125.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Danel, T. et al. (2020). Spatial Graph Convolutional Networks. In: Yang, H., Pasupa, K., Leung, A.CS., Kwok, J.T., Chan, J.H., King, I. (eds) Neural Information Processing. ICONIP 2020. Communications in Computer and Information Science, vol 1333. Springer, Cham. https://doi.org/10.1007/978-3-030-63823-8_76
Download citation
DOI: https://doi.org/10.1007/978-3-030-63823-8_76
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63822-1
Online ISBN: 978-3-030-63823-8
eBook Packages: Computer ScienceComputer Science (R0)