Discriminative structural graph classification

This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions suffer from a dimensionality curse, we consider a restricted setting. In particular, we show that the standard sum and a novel histogram-based function have the capacity to discriminate between any fixed number of inputs chosen by an adversary. Based on our insights, we design a graph neural network aiming, not to maximize discrimination capacity, but to learn discriminative graph representations that generalize well. Our empirical evaluation provides evidence that our choices can yield benefits to the problem of structural graph classification.

[1]  Xiaogang Wang,et al.  Learnable Histogram: Statistical Context Features for Deep Neural Networks , 2016, ECCV.

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

[3]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[4]  Michalis Vazirgiannis,et al.  Matching Node Embeddings for Graph Similarity , 2017, AAAI.

[5]  Natasa Przulj.  Biological network comparison using graphlet degree distribution , 2010, Bioinform..

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

[7]  Yaron Lipman,et al.  On the Universality of Invariant Networks , 2019, ICML.

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

[9]  Geert Leus,et al.  Stochastic graph filtering on time-varying graphs , 2015, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[10]  Samy Bengio,et al.  Order Matters: Sequence to sequence for sets , 2015, ICLR.

[11]  Vijay S. Pande,et al.  Molecular graph convolutions: moving beyond fingerprints , 2016, Journal of Computer-Aided Molecular Design.

[12]  Jan Eric Lenssen,et al.  Fast Graph Representation Learning with PyTorch Geometric , 2019, ArXiv.

[13]  Jure Leskovec,et al.  Inductive Representation Learning on Large Graphs , 2017, NIPS.

[14]  Jure Leskovec,et al.  Learning Structural Node Embeddings via Diffusion Wavelets , 2017, KDD.

[15]  B. Weisfeiler.  On construction and identification of graphs , 1976 .

[16]  G. Lewicki,et al.  Approximation by Superpositions of a Sigmoidal Function , 2003 .

[17]  Gitta Kutyniok,et al.  On the Transferability of Spectral Graph Filters , 2019, 2019 13th International conference on Sampling Theory and Applications (SampTA).

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

[19]  Gabriel Peyré,et al.  Universal Invariant and Equivariant Graph Neural Networks , 2019, NeurIPS.

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

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

[22]  Pierre Vandergheynst,et al.  Compressive Embedding and Visualization using Graphs , 2017, ArXiv.

[23]  Michalis Vazirgiannis,et al.  GraKeL: A Graph Kernel Library in Python , 2018, J. Mach. Learn. Res..

[24]  Inderjit S. Dhillon,et al.  Weighted Graph Cuts without Eigenvectors A Multilevel Approach , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

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

[27]  Jure Leskovec,et al.  How Powerful are Graph Neural Networks? , 2018, ICLR.

[28]  Devdatt P. Dubhashi,et al.  Global graph kernels using geometric embeddings , 2014, ICML.

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

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

[31]  Lorenzo Livi,et al.  Graph Neural Networks With Convolutional ARMA Filters , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Alexandre Tkatchenko,et al.  Quantum-chemical insights from deep tensor neural networks , 2016, Nature Communications.

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

[34]  Yaron Lipman,et al.  Invariant and Equivariant Graph Networks , 2018, ICLR.

[35]  Victor S. Lempitsky,et al.  Learning Deep Embeddings with Histogram Loss , 2016, NIPS.

[36]  Mario Fritz,et al.  See the Difference: Direct Pre-Image Reconstruction and Pose Estimation by Differentiating HOG , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).