Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

NeurIPS 2016  ·  Michaël Defferrard, Xavier Bresson, Pierre Vandergheynst ·

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification CiteSeer (0.5%) ChebyNet Accuracy 45.3% # 10
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Node Classification CiteSeer (1%) ChebyNet Accuracy 59.4% # 10
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Node Classification CiteSeer with Public Split: fixed 20 nodes per class ChebyNet Accuracy 70.1% # 29
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Node Classification Cora (0.5%) ChebyNet Accuracy 33.9% # 15
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Node Classification Cora (1%) ChebyNet Accuracy 44.2% # 15
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Node Classification Cora (3%) ChebyNet Accuracy 62.1% # 14
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Node Classification Cora with Public Split: fixed 20 nodes per class ChebyNet Accuracy 78.0% # 29
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Graph Property Prediction ogbg-molpcba ChebNet Test AP 0.2306 ± 0.0016 # 27
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Validation AP 0.2372 ± 0.0018 # 26
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Number of params 1475003 # 26
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Ext. data No # 1
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Node Classification PubMed (0.03%) ChebyNet Accuracy 45.3% # 14
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Node Classification PubMed (0.05%) ChebyNet Accuracy 48.2% # 14
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Node Classification PubMed (0.1%) ChebyNet Accuracy 55.2% # 14
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Node Classification PubMed with Public Split: fixed 20 nodes per class ChebyNet Accuracy 69.8% # 34
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Skeleton Based Action Recognition SBU ChebyNet Accuracy 96.00% # 4
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Results from Other Papers

Task Dataset Model Metric Name Metric Value Rank Source Paper Compare
Node Classification Citeseer ChebNet Accuracy 69.8% # 58
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Node Classification Cora ChebNet Accuracy 81.2% # 59
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Node Classification Pubmed ChebNet Accuracy 74.4% # 61
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