Fetching the paper…
Reading the bibliography…
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport.
Least squares quantization in PCM
Lloyd, S · 1982
Earlier work this paper cites.
A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) {{O}}(1/k^{2})
Nesterov, Y · 1983
Earlier work this paper cites.
Power diagrams: properties, algorithms and applications
Aurenhammer, F · 1987
Earlier work this paper cites.
Minkowski-type theorems and least-squares partitioning
Aurenhammer, F., Hoffmann, F., and Aronov, B · 1992
Earlier work this paper cites.
Convergence properties of the k-means algorithms
Bottou, L. and Bengio, Y · 1995
Earlier work this paper cites.
A convexity principle for interacting gases
McCann, R. J · 1997
Earlier work this paper cites.
A note on the convergence of the mean shift
Li, X., Hu, Z., and Wu, F · 2007
Earlier work this paper cites.
Long-term planning versus short-term planning in the asymptotical location problem
Brancolini, A., Buttazzo, G., Santambrogio, F., and Stepanov, E · 2009
Earlier work this paper cites.
Optimal Transport: Old and New
Villani, C · 2009
Earlier work this paper cites.
Super-samples from kernel herding
Chen, Y., Welling, M., and Smola, A. J · 2010
Earlier work this paper cites.
Barycenters in the Wasserstein Space
Agueh, M. and Carlier, G · 2011
Earlier work this paper cites.
A multiscale approach to optimal transport
Mérigot, Q · 2011
Cited alongside, same era.
Blue noise through optimal transport
De Goes, F., Breeden, K., Ostromoukhov, V., and Desbrun, M · 2012
Cited alongside, same era.
Approximation by finitely supported measures
Kloeckner, B · 2012
Cited alongside, same era.
Sinkhorn Distances: Lightspeed Computation of Optimal Transport
Cuturi, M · 2013
Cited alongside, same era.
Fast computation of Wasserstein barycenters
Cuturi, M. and Doucet, A · 2014
Cited alongside, same era.
Iterative Bregman Projections for Regularized Transportation Problems
Benamou, J., Carlier, G., Cuturi, M., Nenna, L., and Peyré, G · 2015
Cited alongside, same era.
A Smoothed Dual Approach for Variational Wasserstein Problems
Cuturi, M. and Peyré, G · 2016
Later among the works it cites.
Stochastic Optimization for Large-scale Optimal Transport
Genevay, A., Cuturi, M., Peyré, G., and Bach, F · 2016
Later among the works it cites.
A sparse multiscale algorithm for dense optimal transport
Schmitzer, B · 2016
Later among the works it cites.
Arjovsky, M., Chintala, S., and Bottou, L · 2017
Later among the works it cites.
Sliced wasserstein kernel for persistence diagrams
Carrière, M., Cuturi, M., and Oudot, S · 2017
Later among the works it cites.
Notions of optimal transport theory and how to implement them on a computer
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Lévy, B · 2015
Cited alongside, same era.
Optimal Transport for Applied Mathematicians , volume 87 of Progress in Nonlinear Differential Equations and Their Applications
Santambrogio, F · 2015
Cited alongside, same era.
Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains
Solomon, J., de Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A., Du, T., and Guibas, L · 2015
Cited alongside, same era.
Discrete Wasserstein barycenters: Optimal transport for discrete data
Anderes, E., Borgwardt, S., and Miller, J · 2016
Cited alongside, same era.
Optimal Transport for Domain Adaptation
Courty, N., Flamary, R., Tuia, D., and Rakotomamonjy, A · 2016
Cited alongside, same era.
Convergence of a Newton algorithm for semi-discrete optimal transport
Kitagawa, J., Mérigot, Q., and Thibert, B
Cited in the paper.
Lévy, B. and Schwindt, E · 2017
Later among the works it cites.
Wasserstein dictionary learning: Optimal transport-based unsupervised non-linear dictionary learning
Schmitz, M. A., Heitz, M., Bonneel, N., Mboula, F. M. N., Coeurjolly, D., Cuturi, M., Peyré, G., and Starck, J · 2017
Later among the works it cites.
Parallel streaming Wasserstein barycenters
Staib, M., Claici, S., Solomon, J. M., and Jegelka, S · 2017
Later among the works it cites.
Fast Discrete Distribution Clustering Using Wasserstein Barycenter With Sparse Support
Ye, J., Wu, P., Wang, J. Z., and Li, J · 2017
Later among the works it cites.
Computational Optimal Transport
Peyré, G. and Cuturi, M · 2018
Closest in time.
Optimal Transport on Discrete Domains
Solomon, J · 2018
Closest in time.