Spectral Networks and Locally Connected Networks on Graphs

TL;DR

This paper extends convolutional neural networks to signals on general domains like graphs, introducing spectral and hierarchical clustering methods to enable efficient deep learning on low-dimensional graph data.

Contribution

It proposes two novel generalizations of CNNs for graph-structured data, utilizing hierarchical clustering and spectral graph theory.

Findings

Efficient deep architectures with parameter count independent of input size.

Effective convolutional layers on low-dimensional graphs.

Potential for broader applications in non-Euclidean domains.

Abstract

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.