Convolutional neural networks on irregular domains based on approximate vertex-domain translations

TL;DR

This paper introduces a method to extend convolutional neural networks to irregular graph domains by defining approximate vertex-domain translations, enabling CNN-like operations on non-grid structures.

Contribution

It proposes a novel translation operator on graphs that allows the design of convolutional layers directly in the vertex domain, generalizing CNNs to irregular topologies.

Findings

Successfully designed convolutional layers for irregular graph signals.

Built a CNN that incorporates classical 2D CNN settings as a special case.

Achieved weight sharing directly through vertex domain design.

Abstract

We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of a translation operator on a graph structure. In regular settings such as images, convolutional layers are designed by translating a convolutional kernel over all pixels, thus enforcing translation equivariance. In the case of general graphs however, translation is not a well-defined operation, which makes shifting a convolutional kernel not straightforward. In this article, we introduce a methodology to allow the design of convolutional layers that are adapted to signals evolving on irregular topologies, even in the absence of a natural translation. Using the designed layers, we build a CNN that we train using the initial set of signals. Contrary to other approaches that aim at extending CNNs to irregular domains, we incorporate the classical settings of CNNs for 2D signals as a particular case of our approach. Designing convolutional layers in the vertex domain directly implies weight sharing, which in other approaches is generally estimated a posteriori using heuristics.