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README.md

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[17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/abs/1710.06276). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
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[18] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. (2019). [Optimal Transport for structured data with application on graphs](http://proceedings.mlr.press/v97/titouan19a.html) Proceedings of the 36th International Conference on Machine Learning (ICML).
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[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](https://arxiv.org/abs/1605.08527). Advances in Neural Information Processing Systems (2016).
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[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018)
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[20] Cuturi, M. and Doucet, A. (2014) [Fast Computation of Wasserstein Barycenters](http://proceedings.mlr.press/v32/cuturi14.html). International Conference in Machine Learning
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[21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015). [Convolutional wasserstein distances: Efficient optimal transportation on geometric domains](https://dl.acm.org/citation.cfm?id=2766963). ACM Transactions on Graphics (TOG), 34(4), 66.
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[22] J. Altschuler, J.Weed, P. Rigollet, (2017) [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf), Advances in Neural Information Processing Systems (NIPS) 31
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[23] Aude, G., Peyré, G., Cuturi, M., [Learning Generative Models with Sinkhorn Divergences](https://arxiv.org/abs/1706.00292), Proceedings of the Twenty-First International Conference on Artficial Intelligence and Statistics, (AISTATS) 21, 2018
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[24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. (2019). [Optimal Transport for structured data with application on graphs](http://proceedings.mlr.press/v97/titouan19a.html) Proceedings of the 36th International Conference on Machine Learning (ICML).
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ot/bregman.py

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# Author: Remi Flamary <remi.flamary@unice.fr>
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# Nicolas Courty <ncourty@irisa.fr>
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# Kilian Fatras <kilian.fatras@irisa.fr>
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# Titouan Vayer <titouan.vayer@irisa.fr>
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# License: MIT License
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ot/gromov.py

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log dictionary return only if log==True in parameters
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References
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.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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and Courty Nicolas
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"Optimal Transport for structured data with application on graphs"
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International Conference on Machine Learning (ICML). 2019.
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Ms : all distance matrices between the feature of the barycenter and the other features dist(X,Ys) shape (N,ns)
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References
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.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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and Courty Nicolas
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"Optimal Transport for structured data with application on graphs"
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International Conference on Machine Learning (ICML). 2019.
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References
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.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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and Courty Nicolas
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"Optimal Transport for structured data with application on graphs"
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International Conference on Machine Learning (ICML). 2019.

ot/optim.py

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The value of the cost for the next iteration
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References
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.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
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and Courty Nicolas
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"Optimal Transport for structured data with application on graphs"
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International Conference on Machine Learning (ICML). 2019.

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