Signal Processing - July 2017 - 18
Michael M. Bronstein, Joan Bruna, Yann LeCun,
Arthur Szlam, and Pierre Vandergheynst
M
any 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.
Geometric deep learning is an umbrella term for emerging
techniques attempting to generalize (structured) deep neural models to non-Euclidean domains, such as graphs and manifolds. The
purpose of this article is to overview different examples of geometric
deep-learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
Overview of deep learning
Deep learning refers to learning complicated concepts by building them from
simpler ones in a hierarchical or multilayer manner. Artificial neural networks are
popular realizations of such deep multilayer hierarchies. In the past few years, the growing
computational power of modern graphics processing unit (GPU)-based computers and the availability of large training data sets have allowed successfully training neural networks with many layers
and degrees of freedom (DoF) [1]. This has led to qualitative breakthroughs on a wide variety of tasks, from
speech recognition [2], [3] and machine translation [4] to image analysis and computer vision [5]-[11] (see [12]
Geometric Deep Learning
Going beyond Euclidean data
Digital Object Identifier 10.1109/MSP.2017.2693418
Date of publication: 11 July 2017
18
©ISTOCKPHOTO.COM/LIUZISHAN
IEEE SIGNAL PROCESSING MAGAZINE
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July 2017
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Table of Contents for the Digital Edition of Signal Processing - July 2017
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