In the last years, Graph Convolutional Neural Networks gained popularity in the Machine Learning community for their capability of extracting local compositional features on signals defined on non-Euclidean domains. Shape correspondence, document classification, molecular properties predictions are just few of the many different problems where these techniques have been successfully applied. In this talk we will present Deep Geometric Matrix Completion, a recent application of Graph Convolutional Neural Networks to the matrix completion problem. We will review spectral approaches (briefly highlighting pros and cons of different solutions and presenting a recent GCN with spectral zoom properties, CayleyNet), we will introduce MGCNN (a Multi-Graph Convolutional Neural Network able to deal with signals defined over multiple graphs)and we will show how coupling such technique with a RNN, a learnable diffusion process can be realized for reconstructing missing information. This particular approach appears as the first attempt of applying GCNs to the matrix completion problem. Extensive experimental evaluation shows how Geometric Deep Learning techniques allow to outperform previous state of the art solutions on matrix completion tasks.
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