Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of the social graph. Sensor networks are graph models of distributed interconnected sensors, whose readings are modelled as time-dependent signals on the vertices. In genetics, gene expression data are modeled as signals defined on the regulatory network. In neuroscience, graph models are used to represent anatomical and functional structures of the brain. Modeling data given as points in a high-dimensional Euclidean space using nearest neighbor graphs is an increasingly popular trend in data science, allowing practitioners access to the intrinsic structure of the data. In computer graphics and vision, 3D objects are modeled as Riemannian manifolds (surfaces) endowed with properties such as color texture. Even more complex examples include networks of operators, e.g., functional correspondences or difference operators in a collection of 3D shapes, or orientations of overlapping cameras in multi-view vision ("structure from motion") problems. The complexity of geometric data and the availability of very large datasets (in the case of social networks, on the scale of billions) suggest the use of machine learning techniques. In particular, deep learning has recently proven to be a powerful tool for problems with large datasets with underlying Euclidean structure. The purpose of this paper is to overview the problems arising in relation to geometric deep learning and present solutions existing today for this class of problems, as well as key difficulties and future research directions.

本文主要探讨了几种几何深度学习问题以及目前存在的解决方案、主要困难、应用和未来研究方向。这些问题涉及非欧几里得域，需要使用结构化的深度神经模型来解决。

几何深度学习：超越欧几里德数据