000223439 001__ 223439
000223439 005__ 20190617200523.0
000223439 0247_ $$a10.1109/Msp.2017.2693418$$2doi
000223439 02470 $$2ISI$$a000405179500007
000223439 02470 $$2ArXiv$$a1611.08097
000223439 037__ $$aARTICLE
000223439 245__ $$aGeometric deep learning: going beyond Euclidean data
000223439 260__ $$c2017
000223439 269__ $$a2017
000223439 300__ $$a25
000223439 336__ $$aJournal Articles
000223439 520__ $$aMany signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of the social graph [1]. Sensor networks are graph models of distributed interconnected sensors, whose readings are modelled as time-dependent signals on the vertices. In genetics, gene expression data are modeled as signals defined on the regulatory network [2]. In neuroscience, graph models are used to represent anatomical and functional structures of the brain. In computer graphics and vision, 3D objects are modeled as Riemannian manifolds (surfaces) endowed with properties such as color texture. Even more complex examples include networks of operators, e.g., functional correspondences [3] or difference operators [4] in a collection of 3D shapes, or orientations of overlapping cameras in multi-view vision (“structure from motion”) problems [5]. The complexity of geometric data and the availability of very large datasets (in the case of social networks, on the scale of billions) suggest the use of machine learning techniques. In particular, deep learning has recently proven to be a powerful tool for problems with large datasets with underlying Euclidean structure. The purpose of this paper is to overview the problems arising in relation to geometric deep learning and present solutions existing today for this class of problems, as well as key difficulties and future research directions.
000223439 6531_ $$adeep learning
000223439 6531_ $$aartificial intelligence
000223439 6531_ $$amachine learning
000223439 6531_ $$adifferential geometry
000223439 700__ $$aBronstein, M.
000223439 700__ $$aBruna, J.
000223439 700__ $$aLeCun, Y.
000223439 700__ $$aSzlam, A.
000223439 700__ $$g120906$$aVandergheynst, Pierre$$0240428
000223439 773__ $$q18-42$$k4$$j34$$tIEEE Signal Processing Magazine
000223439 8564_ $$uhttps://arxiv.org/pdf/1611.08097v1.pdf$$zURL
000223439 8564_ $$uhttps://infoscience.epfl.ch/record/223439/files/1611.08097v1.pdf$$zPreprint$$s4242736$$yPreprint
000223439 8560_ $$falain.borel@epfl.ch
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000223439 917Z8 $$x120906
000223439 937__ $$aEPFL-ARTICLE-223439
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