Geometric Deep Learning: Going beyond Euclidean data

Michael M. Bronstein, Joan Bruna Estrach, Yann LeCun, Arthur Szlam, Pierre Vandergheynst

Research output: Contribution to journalReview article

Abstract

Many scientific fields study data with an underlying structure that is non-Euclidean. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions) and are natural targets for machine-learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural-language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure and in cases where the invariances of these structures are built into networks used to model them.

Original languageEnglish (US)
Article number7974879
Pages (from-to)18-42
Number of pages25
JournalIEEE Signal Processing Magazine
Volume34
Issue number4
DOIs
StatePublished - Jul 1 2017

Fingerprint

Euclidean
Social Networks
Social sciences
Computer graphics
Invariance
Computer vision
Sensor networks
Learning systems
Brain
Field Study
Regulatory Networks
Social Sciences
Imaging techniques
Computer Vision
Natural Language
Sensor Networks
Communication
Machine Learning
Processing
Imaging

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

Bronstein, M. M., Bruna Estrach, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017). Geometric Deep Learning: Going beyond Euclidean data. IEEE Signal Processing Magazine, 34(4), 18-42. [7974879]. https://doi.org/10.1109/MSP.2017.2693418

Geometric Deep Learning : Going beyond Euclidean data. / Bronstein, Michael M.; Bruna Estrach, Joan; LeCun, Yann; Szlam, Arthur; Vandergheynst, Pierre.

In: IEEE Signal Processing Magazine, Vol. 34, No. 4, 7974879, 01.07.2017, p. 18-42.

Research output: Contribution to journalReview article

Bronstein, MM, Bruna Estrach, J, LeCun, Y, Szlam, A & Vandergheynst, P 2017, 'Geometric Deep Learning: Going beyond Euclidean data', IEEE Signal Processing Magazine, vol. 34, no. 4, 7974879, pp. 18-42. https://doi.org/10.1109/MSP.2017.2693418
Bronstein MM, Bruna Estrach J, LeCun Y, Szlam A, Vandergheynst P. Geometric Deep Learning: Going beyond Euclidean data. IEEE Signal Processing Magazine. 2017 Jul 1;34(4):18-42. 7974879. https://doi.org/10.1109/MSP.2017.2693418
Bronstein, Michael M. ; Bruna Estrach, Joan ; LeCun, Yann ; Szlam, Arthur ; Vandergheynst, Pierre. / Geometric Deep Learning : Going beyond Euclidean data. In: IEEE Signal Processing Magazine. 2017 ; Vol. 34, No. 4. pp. 18-42.
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