Graph matching as a graph convolution operator for graph neural networks

Abstract

Convolutional neural networks (CNNs), in a few decades, have outperformed the existing state of the art methods in classication context. However, in the way they were formalised, CNNs are bound to operate on euclidean spaces. Indeed, convolution is a signal operation that are dened on euclidean spaces. This has restricted deep learning main use to euclidean-dened data such as sound or image. And yet, numerous computer application elds (among which network analysis, computational social science, chemo-informatics or computer graphics) induce non-euclideanly dened data such as graphs, networks or manifolds. In this paper we propose a new convolution neural network architecture, dened directly into graph space. The convolution operator is dened in graph domain thanks to a graph matching procedure between the input signal and a lter. We show its usability in a back-propagation context. Experimental results show that our model performance is at state of the art level on simple tasks. It shows robustness with respect to graph domain changes and improvement with respect to other euclidean and non-euclidean convolutional architectures.

Graphs in pattern recognition: successes, shortcomings, and perspectives

“…There are many properties of chemical compounds that are dependent on the structure of the components; problems related to these properties (searching for molecules that have similar properties, searching for chemical components that have a particular action such as carcinogenicity, etc.) are therefore solved through GM 46 – 48 or even graph embedding techniques 4 . Some of classical datasets in this domain are briefly described below.…”