Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

TL;DR

This paper extends convolutional neural networks to irregular graph domains using spectral graph theory, enabling efficient localized filtering with linear complexity, demonstrated on image and text datasets.

Contribution

It introduces a spectral graph CNN framework that generalizes classical CNNs to arbitrary graphs with efficient, localized filters and constant learning complexity.

Findings

Successfully applied to MNIST and 20NEWS datasets.

Achieves local, stationary, and compositional feature learning on graphs.

Maintains linear computational complexity similar to classical CNNs.

Abstract

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.