Graph Capsule Convolutional Neural Networks

Graph Convolutional Neural Networks (GCNNs) are the most recent exciting advancement in deep learning field and their applications are quickly spreading in multi-cross-domains including bioinformatics, chemoinformatics, social networks, natural language processing and computer vision. In this paper, we expose and tackle some of the basic weaknesses of a GCNN model with a capsule idea presented in \cite{hinton2011transforming} and propose our Graph Capsule Network (GCAPS-CNN) model. In addition, we design our GCAPS-CNN model to solve especially graph classification problem which current GCNN models find challenging. Through extensive experiments, we show that our proposed Graph Capsule Network can significantly outperforms both the existing state-of-art deep learning methods and graph kernels on graph classification benchmark datasets.

[1]  Risi Kondor,et al.  The Multiscale Laplacian Graph Kernel , 2016, NIPS.

[2]  Zhi-Li Zhang,et al.  Hunt For The Unique, Stable, Sparse And Fast Feature Learning On Graphs , 2017, NIPS.

[3]  Karsten M. Borgwardt,et al.  The graphlet spectrum , 2009, ICML '09.

[4]  Hisashi Kashima,et al.  Marginalized Kernels Between Labeled Graphs , 2003, ICML.

[5]  Risi Kondor,et al.  Covariant Compositional Networks For Learning Graphs , 2018, ICLR.

[6]  Regina Barzilay,et al.  Deriving Neural Architectures from Sequence and Graph Kernels , 2017, ICML.

[7]  Bo Zong,et al.  Substructure Assembling Network for Graph Classification , 2018, AAAI.

[8]  Kurt Mehlhorn,et al.  Efficient graphlet kernels for large graph comparison , 2009, AISTATS.

[9]  Geoffrey E. Hinton,et al.  Transforming Auto-Encoders , 2011, ICANN.

[10]  Nikos Komodakis,et al.  Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[11]  Le Song,et al.  Discriminative Embeddings of Latent Variable Models for Structured Data , 2016, ICML.

[12]  Roman Garnett,et al.  Efficient Graph Kernels by Randomization , 2012, ECML/PKDD.

[13]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[14]  Tony Jebara,et al.  A Kernel Between Sets of Vectors , 2003, ICML.

[15]  Nils M. Kriege,et al.  On Valid Optimal Assignment Kernels and Applications to Graph Classification , 2016, NIPS.

[16]  Joan Bruna,et al.  Spectral Networks and Locally Connected Networks on Graphs , 2013, ICLR.

[17]  Donald F. Towsley,et al.  Diffusion-Convolutional Neural Networks , 2015, NIPS.

[18]  Gerben de Vries.  A Fast Approximation of the Weisfeiler-Lehman Graph Kernel for RDF Data , 2013, ECML/PKDD.

[19]  Pinar Yanardag,et al.  Deep Graph Kernels , 2015, KDD.

[20]  Joan Bruna,et al.  Deep Convolutional Networks on Graph-Structured Data , 2015, ArXiv.

[21]  Samuel S. Schoenholz,et al.  Neural Message Passing for Quantum Chemistry , 2017, ICML.

[22]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[23]  Xavier Bresson,et al.  CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters , 2017, IEEE Transactions on Signal Processing.

[24]  Mathias Niepert,et al.  Learning Convolutional Neural Networks for Graphs , 2016, ICML.

[25]  Thomas Gärtner,et al.  On Graph Kernels: Hardness Results and Efficient Alternatives , 2003, COLT.

[26]  Andreas Ziehe,et al.  Learning Invariant Representations of Molecules for Atomization Energy Prediction , 2012, NIPS.

[27]  Natasa Przulj,et al.  Biological network comparison using graphlet degree distribution , 2007, Bioinform..

[28]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[29]  Mathias Niepert,et al.  Learning Graph Representations with Embedding Propagation , 2017, NIPS.

[30]  Kurt Mehlhorn,et al.  Weisfeiler-Lehman Graph Kernels , 2011, J. Mach. Learn. Res..

[31]  Alán Aspuru-Guzik,et al.  Convolutional Networks on Graphs for Learning Molecular Fingerprints , 2015, NIPS.

[32]  Marleen de Bruijne,et al.  Scalable kernels for graphs with continuous attributes , 2013, NIPS.

[33]  Karsten M. Borgwardt,et al.  The skew spectrum of graphs , 2008, ICML '08.

[34]  Luc De Raedt,et al.  Graph Invariant Kernels , 2015, IJCAI.

[35]  Yixin Chen,et al.  An End-to-End Deep Learning Architecture for Graph Classification , 2018, AAAI.

[36]  Geoffrey E. Hinton,et al.  Dynamic Routing Between Capsules , 2017, NIPS.

[37]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.