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Deep learning has achieved a remarkable performance breakthrough in severalfields, most notably in speech recognition, natural language processing, andcomputer vision. In particular, convolutional neural network (CNN)architectures currently produce state-of-the-art performance on a variety ofimage analysis tasks such as object detection and recognition. Most of deeplearning research has so far focused on dealing with 1D, 2D, or 3DEuclidean-structured data such as acoustic signals, images, or videos.Recently, there has been an increasing interest in geometric deep learning,attempting to generalize deep learning methods to non-Euclidean structured datasuch as graphs and manifolds, with a variety of applications from the domainsof network analysis, computational social science, or computer graphics. Inthis paper, we propose a unified framework allowing to generalize CNNarchitectures to non-Euclidean domains (graphs and manifolds) and learn local,stationary, and compositional task-specific features. We show that variousnon-Euclidean CNN methods previously proposed in the literature can beconsidered as particular instances of our framework. We test the proposedmethod on standard tasks from the realms of image-, graph- and 3D shapeanalysis and show that it consistently outperforms previous approaches.

Geometric deep learning on graphs and manifolds using mixture model CNNs