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.

翻译：卷积神经网络（CNN）在近几十年来已在分类任务中超越了现有最先进方法。然而，在其形式化框架下，CNN仅限于在欧几里得空间中运行。事实上，卷积是一种定义在欧几里得空间上的信号运算。这导致深度学习主要应用于声音、图像等欧几里得定义的数据。然而，众多计算机应用领域（包括网络分析、计算社会科学、化学信息学或计算机图形学）会生成非欧几里得定义的数据，如图结构、网络或流形。本文提出了一种新型卷积神经网络架构，其直接定义在图空间之中。我们将卷积和池化算子定义于图域，并展示了其在反向传播场景中的可用性。实验结果表明，该模型在简单任务上的性能达到当前最优水平。该模型对图域变化具有鲁棒性，且在与其他欧几里得及非欧几里得卷积架构的对比中展现出显著改进。