Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
This work addresses the challenge of applying CNNs to high-dimensional irregular data like social networks or brain connectomes, representing a novel method for a known bottleneck in graph-based deep learning.
The authors tackled the problem of extending convolutional neural networks from regular grids to irregular graph domains by proposing a formulation based on spectral graph theory, achieving linear computational complexity and demonstrating the system's ability to learn local features on graphs in experiments on MNIST and 20NEWS.
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.