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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

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arxiv 1606.09375 v3 pith:5WOS6X2T submitted 2016-06-30 cs.LG stat.ML

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

classification cs.LG stat.ML
keywords graphscnnsconvolutionalnetworkscomplexityfastgraphlearning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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