Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs

CVPR 2017  ·  Martin Simonovsky, Nikos Komodakis ·

A number of problems can be formulated as prediction on graph-structured data. In this work, we generalize the convolution operator from regular grids to arbitrary graphs while avoiding the spectral domain, which allows us to handle graphs of varying size and connectivity. To move beyond a simple diffusion, filter weights are conditioned on the specific edge labels in the neighborhood of a vertex. Together with the proper choice of graph coarsening, we explore constructing deep neural networks for graph classification. In particular, we demonstrate the generality of our formulation in point cloud classification, where we set the new state of the art, and on a graph classification dataset, where we outperform other deep learning approaches. The source code is available at https://github.com/mys007/ecc

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification D&D ECC (5 scores) Accuracy 74.1% # 40
Graph Classification ENZYMES ECC (5 scores) Accuracy 52.67% # 31
3D Object Classification ModelNet10 ECC (12 votes) Accuracy 90 # 4
3D Object Classification ModelNet40 ECC (12 votes) Classification Accuracy 83.2 # 7
3D Point Cloud Classification ModelNet40 ECC Overall Accuracy 87.4 # 97
Mean Accuracy 83.2 # 34
Graph Classification MUTAG ECC (5 scores) Accuracy 88.33% # 38
Graph Classification NCI1 ECC (5 scores) Accuracy 83.8% # 18
Graph Classification NCI109 ECC (5 scores) Accuracy 82.14 # 11
3D Point Cloud Classification Sydney Urban Objects ECC F1 78.4 # 1