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We present a novel framework based on optimal transport for the challenging problem of comparing graphs.
On the transfer of masses: Doklady akademii nauk ussr
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Collective dynamics of ‘small-world’networks
D. J. Watts and S. H. Strogatz · 1998
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Generating random regular graphs quickly
A. Steger and N. C. Wormald · 1999
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Emergence of scaling in random networks
A.-L. Barabási and R. Albert · 1999
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Semi-supervised learning using gaussian fields and harmonic functions
X. Zhu, Z. Ghahramani, and J. D. Lafferty · 2003
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An eigenspace projection clustering method for inexact graph matching
T. Caelli and S. Kosinov · 2004
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Probabilistic subgraph matching based on convex relaxation
C. Schellewald and C. Schnörr · 2005
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Gaussian Markov random fields: theory and applications
Havard Rue and Leonhard Held · 2005
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Balanced graph matching
P. Srinivasan, T. Cour, and J. Shi · 2007
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Optimal transport: old and new , volume 338
C. Villani · 2008
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Sparse inverse covariance estimation with the graphical lasso
J. Friedman, T. Hastie, and R. Tibshirani · 2008
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An integer projected fixed point method for graph matching and map inference
M. Leordeanu, M. Hebert, and R. Sukthankar · 2009
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Reweighted random walks for graph matching
M. Cho, J. Lee, and K. M. Lee · 2010
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Gromov–wasserstein distances and the metric approach to object matching
F. Mémoli · 2011
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Wasserstein geometry of gaussian measures
A. Takatsu · 2011
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Spectral distances of graphs
I. Jovanović and Z. Stanić · 2012
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Regularized discrete optimal transport
S. Ferradans, N. Papadakis, J. Rabin, G. Peyré, and J.-F. Aujol · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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Deformable graph matching
F. Zhou and F. De la Torre · 2013
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Optimal transport with Laplacian regularization
R. Flamary, N. Courty, A. Rakotomamonjy, and D. Tuia · 2014
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Matching node embeddings for graph similarity
G. Nikolentzos, P. Meladianos, and M. Vazirgiannis · 2017
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Network topology inference from spectral templates
S. Segarra, A. G. Marques, G. Mateos, and A. Ribeiro · 2017
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Variational adaptive-newton method for explorative learning
M. E. Khan, W. Lin, V. Tangkaratt, Z. Liu, and D. Nielsen · 2017
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Improved bilinear pooling with CNNs
T.-Y. Lin and S. Maji · 2017
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Identifying network structure similarity using spectral graph theory
R. Gera, L. Alonso, B. Crawford, J. House, J. A. Mendez-Bermudez, T. Knuth, and R. Miller · 2018
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D. P. Kingma and M. Welling · 2014
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On convex relaxation of graph isomorphism
Yonathan Aflalo, Alexander Bronstein, and Ron Kimmel · 2015
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On spectral properties for graph matching and graph isomorphism problems
Marcelo Fiori and Guillermo Sapiro · 2015
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Spectral distances on graphs
J. Gu, B. Hua, and S. Liu · 2015
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Robust principal component analysis on graphs
N. Shahid, V. Kalofolias, X. Bresson, M. Bronstein, and P. Vandergheynst · 2015
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A short survey of recent advances in graph matching
J. Yan, X. Yin, W. Lin, C. Deng, H. Zha, and X. Yang · 2016
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G. Peyré and M. Cuturi · 2018
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Generalizing graph matching beyond quadratic assignment model
T. Yu, J. Yan, Y. Wang, W. Liu, and B. Li · 2018
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Learning latent permutations with gumbel-sinkhorn networks
G. Mena, D. Belanger, S. Linderman, and J. Snoek · 2018
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Learning permutations with sinkhorn policy gradient
P. Emami and S. Ranka · 2018
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Gromov-wasserstein alignment of word embedding spaces
D. Alvarez-Melis and T. S. Jaakkola · 2018
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Optimal transport for structured data
T. Vayer, L. Chapel, R. Flamary, R. Tavenard, and N. Courty · 2018
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Learning graphs from data: A signal representation perspective
X. Dong, D. Thanou, M. Rabbat, and P. Frossard · 2018
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Learning generative models with sinkhorn divergences
A. Genevay, G Peyré, and M. Cuturi · 2018
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Differential properties of sinkhorn approximation for learning with wasserstein distance
G. Luise, A. Rudi, M. Pontil, and C. Ciliberto · 2018
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Implicit reparameterization gradients
M. Figurnov, S. Mohamed, and A. Mnih · 2018
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On the convergence of adam and beyond
Sashank J. Reddi, Satyen Kale, and Sanjiv Kumar · 2018
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Netlsd: hearing the shape of a graph
Anton Tsitsulin, Davide Mottin, Panagiotis Karras, Alexander Bronstein, and Emmanuel Müller · 2018
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