  Convolutional neural networks (CNNs), in a few decades, have outperformed the
existing state of the art methods in classification context. However, in the
way they were formalised, CNNs are bound to operate on euclidean spaces.
Indeed, convolution is a signal operation that are defined on euclidean spaces.
This has restricted deep learning main use to euclidean-defined data such as
sound or image. And yet, numerous computer application fields (among which
network analysis, computational social science, chemo-informatics or computer
graphics) induce non-euclideanly defined data such as graphs, networks or
manifolds. In this paper we propose a new convolution neural network
architecture, defined directly into graph space. Convolution and pooling
operators are defined in graph domain. 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.
