On Filter Size in Graph Convolutional Networks

Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional filters over multi-dimensional tensors. In particular, we derive a simple, efficient and effective way to introduce a hyper-parameter on graph convolutions that influences the filter size, i.e., its receptive field over the considered graph. We show with experimental results on real-world graph datasets that the proposed graph convolutional filter improves the predictive performance of Deep Graph Convolutional Networks.

[1]  Laurens van der Maaten,et al.  Learning Discriminative Fisher Kernels , 2011, ICML.

[2]  Fabrizio Costa,et al.  Fast Neighborhood Subgraph Pairwise Distance Kernel , 2010, ICML.

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

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

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

[6]  Tomaso A. Poggio,et al.  Bridging the Gaps Between Residual Learning, Recurrent Neural Networks and Visual Cortex , 2016, ArXiv.

[7]  P. Dobson,et al.  Distinguishing enzyme structures from non-enzymes without alignments. , 2003, Journal of molecular biology.

[8]  Ashwin Srinivasan,et al.  Statistical Evaluation of the Predictive Toxicology Challenge 2000-2001 , 2003, Bioinform..

[9]  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).

[10]  Alessio Micheli,et al.  Neural Network for Graphs: A Contextual Constructive Approach , 2009, IEEE Transactions on Neural Networks.

[11]  Alessandro Sperduti,et al.  Ordered Decompositional DAG kernels enhancements , 2015, Neurocomputing.

[12]  Dumitru Erhan,et al.  Going deeper with convolutions , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[13]  Xavier Bresson,et al.  An Experimental Study of Neural Networks for Variable Graphs , 2018, ICLR.

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

[15]  Ah Chung Tsoi,et al.  The Graph Neural Network Model , 2009, IEEE Transactions on Neural Networks.

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

[17]  Alessandro Sperduti,et al.  A Tree-Based Kernel for Graphs , 2012, SDM.

[18]  Markus Hagenbuchner,et al.  Learning Nonsparse Kernels by Self-Organizing Maps for Structured Data , 2009, IEEE Transactions on Neural Networks.

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

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

[21]  S. V. N. Vishwanathan,et al.  Graph kernels , 2007 .

[22]  Hans-Peter Kriegel,et al.  Shortest-path kernels on graphs , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[23]  Alessandro Sperduti,et al.  Supervised neural networks for the classification of structures , 1997, IEEE Trans. Neural Networks.

[24]  Pietro Liò,et al.  Graph Attention Networks , 2017, ICLR.

[25]  Jure Leskovec,et al.  Representation Learning on Graphs: Methods and Applications , 2017, IEEE Data Eng. Bull..

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

[27]  Davide Bacciu,et al.  Generative Kernels for Tree-Structured Data , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[28]  George Karypis,et al.  Comparison of descriptor spaces for chemical compound retrieval and classification , 2006, Sixth International Conference on Data Mining (ICDM'06).

[29]  Alessandro Sperduti,et al.  Graph Kernels Exploiting Weisfeiler-Lehman Graph Isomorphism Test Extensions , 2014, ICONIP.

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

[31]  A. Debnath,et al.  Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. Correlation with molecular orbital energies and hydrophobicity. , 1991, Journal of medicinal chemistry.

[32]  K. G. Srinivasa,et al.  Representation Learning on Graphs , 2018 .

[33]  Joonseok Lee,et al.  N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification , 2018, UAI.

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

[35]  Richard S. Zemel,et al.  Gated Graph Sequence Neural Networks , 2015, ICLR.