  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.
