This manuscript sums up our work on extending convolutional neuralnetworks to irregular domains through graph inference. It consists of three main chapters, each giving the details of a part of a methodology allowing the definition of such networks to process signals evolving on graphs with unknown structures.First, graph inference from data is explored, in order to provide a graph modeling the support of the signals to classify. Second, translation operators that preserve neighborhood properties of the vertices are identified on the inferred graph. Third, these translations are used to shift a convolutional kernel on the graph in order to define a convolutional neural network that is adapted to the input data.We have illustrated our methodology on a dataset of images. While not using any particular knowledge on the signals, we have been able to infer a graph that is close to a grid. Translations on this graph resemble Euclidean translations. Therefore, this has allowed us to define an adapted convolutional neural network that is very close what one would obtain when using the information that signals are images. This network, trained on the initial data, has out performed state of the art methods by more than 13 points, while using a very simple and easily improvable architecture.The method we have introduced is a generalization of convolutional neural networks. As a matter of fact, they can be seen as aparticularization of our approach in the case where the graph is a grid. Our work thus opens the way to numerous perspectives, as it provides an efficient way to build networks that are adapted to the data.