On convolution of graph signals and deep learning on graph domains

Abstract : Convolutional neural networks have proven to be the deep learning model that performs best on regularly structured datasets like images or sounds. However, they cannot be applied on datasets with an irregular structure (e.g. sensor networks, citation networks, MRIs). In this thesis, we develop an algebraic theory of convolutions on irregular domains. We construct a family of convolutions that are based on group actions (or, more generally, groupoid actions) that acts on the vertex domain and that have properties that depend on the edges. With the help of these convolutions, we propose extensions of convolutional neural netowrks to graph domains. Our researches lead us to propose a generic formulation of the propagation between layers, that we call the neural contraction. From this formulation, we derive many novel neural network models that can be applied on irregular domains. Through benchmarks and experiments, we show that they attain state-of-the-art performances, and beat them in some cases.
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Jean-Charles Vialatte. On convolution of graph signals and deep learning on graph domains. Artificial Intelligence [cs.AI]. Ecole nationale supérieure Mines-Télécom Atlantique, 2018. English. ⟨NNT : 2018IMTA0118⟩. ⟨tel-02136338⟩

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