TY - JOUR
T1 - CayleyNets
T2 - Graph Convolutional Neural Networks with Complex Rational Spectral Filters
AU - Levie, Ron
AU - Monti, Federico
AU - Bresson, Xavier
AU - Bronstein, Michael M.
N1 - Funding Information: Manuscript received March 6, 2018; revised July 16, 2018, August 21, 2018, and October 18, 2018; accepted October 26, 2018. Date of publication November 5, 2018; date of current version November 20, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Pierre Borgnat. The work of F. Monti and M. M. Bronstein was supported in part by the ERC Consolidator Grant 724228 (LEMAN), in part by the Google Faculty Research Awards, in part by the Amazon AWS ML Research Award, in part by the Royal Society Wolfson Research Merit Award, and in part by the Rudolf Diesel fellowship at the Institute for Advanced Studies, TU Munich. The work of X. Bresson was supported by the NRF Fellowship NRFF2017-10. (Ron Levie and Federico Monti contributed equally to this work.) (Corresponding author: Ron Levie.) R. Levie is with the Institute of Mathematics, Technische Universität Berlin, Berlin 10623, Germany (e-mail:,[email protected]). Publisher Copyright: © 1991-2012 IEEE.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification, and matrix completion tasks.
AB - The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification, and matrix completion tasks.
KW - Geometric deep learning
KW - graph convolution neural networks
KW - graph giltering
KW - spectral approaches
UR - https://www.scopus.com/pages/publications/85056170412
U2 - 10.1109/TSP.2018.2879624
DO - 10.1109/TSP.2018.2879624
M3 - Article
SN - 1053-587X
VL - 67
SP - 97
EP - 109
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 1
M1 - 8521593
ER -