A Convolutional Neural Network into graph space
This addresses the problem of applying deep learning to non-Euclidean data like graphs, which is crucial for fields such as network analysis and chemo-informatics, representing an incremental advancement in adapting CNNs to new domains.
The paper tackles the limitation of CNNs to Euclidean data by proposing a new CNN architecture defined directly in graph space, with convolution and pooling operators adapted for graphs, achieving state-of-the-art performance on simple tasks and showing robustness to graph domain changes.
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.