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‎master/_downloads/00efe738b664431523810a0d0baf5949/plot_lowrank_GW.ipynb‎

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"\n# Low rank Gromov-Wasterstein between samples\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.9.4.</p></div>\n\nComparison between entropic Gromov-Wasserstein and Low Rank Gromov Wasserstein [67]\non two curves in 2D and 3D, both sampled with 200 points.\n\nThe squared Euclidean distance is considered as the ground cost for both samples.\n\n[67] Scetbon, M., Peyr\u00e9, G. & Cuturi, M. (2022).\n\"Linear-Time GromovWasserstein Distances using Low Rank Couplings and Costs\".\nIn International Conference on Machine Learning (ICML), 2022.\n"
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"\n# Low rank Gromov-Wasterstein between samples\n\n<div class=\"alert alert-info\"><h4>Note</h4>\n\nExample added in release: 0.9.4.\n\n</div>\n\nComparison between entropic Gromov-Wasserstein and Low Rank Gromov Wasserstein [67]\non two curves in 2D and 3D, both sampled with 200 points.\n\nThe squared Euclidean distance is considered as the ground cost for both samples.\n\n[67] Scetbon, M., Peyr\u00e9, G. & Cuturi, M. (2022).\n\"Linear-Time GromovWasserstein Distances using Low Rank Couplings and Costs\".\nIn International Conference on Machine Learning (ICML), 2022.\n"
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‎master/_downloads/01f7e78349daa20a31a00f8d86852f5e/plot_partial_1d.ipynb‎

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‎master/_downloads/059a63fc6cb655dcd2f1c9a61bb9d7ec/plot_OT_2D_samples.ipynb‎

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‎master/_downloads/0dbd57c6090215001a0a712021c577e5/plot_GMMOT_plan.ipynb‎

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‎master/_downloads/0e0c970a6374049b6079f4ba3f451631/plot_fgw_solvers.ipynb‎

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"\n# Comparison of Fused Gromov-Wasserstein solvers\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.9.1.</p></div>\n\nThis example illustrates the computation of FGW for attributed graphs\nusing 4 different solvers to estimate the distance based on Conditional\nGradient [24], Sinkhorn projections [12, 51] and alternated Bregman\nprojections [63, 64].\n\nWe generate two graphs following Stochastic Block Models further endowed with\nnode features and compute their FGW matchings.\n\n[12] Gabriel Peyr\u00e9, Marco Cuturi, and Justin Solomon (2016),\n\"Gromov-Wasserstein averaging of kernel and distance matrices\".\nInternational Conference on Machine Learning (ICML).\n\n[24] Vayer Titouan, Chapel Laetitia, Flamary R\u00e9mi, Tavenard Romain\nand Courty Nicolas\n\"Optimal Transport for structured data with application on graphs\"\nInternational Conference on Machine Learning (ICML). 2019.\n\n[51] Xu, H., Luo, D., Zha, H., & Carin, L. (2019).\n\"Gromov-wasserstein learning for graph matching and node embedding\".\nIn International Conference on Machine Learning (ICML), 2019.\n\n[63] Li, J., Tang, J., Kong, L., Liu, H., Li, J., So, A. M. C., & Blanchet, J.\n\"A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in\nGraph Data\". International Conference on Learning Representations (ICLR), 2023.\n\n[64] Ma, X., Chu, X., Wang, Y., Lin, Y., Zhao, J., Ma, L., & Zhu, W.\n\"Fused Gromov-Wasserstein Graph Mixup for Graph-level Classifications\".\nIn Thirty-seventh Conference on Neural Information Processing Systems\n(NeurIPS), 2023.\n"
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"\n# Comparison of Fused Gromov-Wasserstein solvers\n\n<div class=\"alert alert-info\"><h4>Note</h4>\n\nExample added in release: 0.9.1.\n\n</div>\n\nThis example illustrates the computation of FGW for attributed graphs\nusing 4 different solvers to estimate the distance based on Conditional\nGradient [24], Sinkhorn projections [12, 51] and alternated Bregman\nprojections [63, 64].\n\nWe generate two graphs following Stochastic Block Models further endowed with\nnode features and compute their FGW matchings.\n\n[12] Gabriel Peyr\u00e9, Marco Cuturi, and Justin Solomon (2016),\n\"Gromov-Wasserstein averaging of kernel and distance matrices\".\nInternational Conference on Machine Learning (ICML).\n\n[24] Vayer Titouan, Chapel Laetitia, Flamary R\u00e9mi, Tavenard Romain\nand Courty Nicolas\n\"Optimal Transport for structured data with application on graphs\"\nInternational Conference on Machine Learning (ICML). 2019.\n\n[51] Xu, H., Luo, D., Zha, H., & Carin, L. (2019).\n\"Gromov-wasserstein learning for graph matching and node embedding\".\nIn International Conference on Machine Learning (ICML), 2019.\n\n[63] Li, J., Tang, J., Kong, L., Liu, H., Li, J., So, A. M. C., & Blanchet, J.\n\"A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in\nGraph Data\". International Conference on Learning Representations (ICLR), 2023.\n\n[64] Ma, X., Chu, X., Wang, Y., Lin, Y., Zhao, J., Ma, L., & Zhu, W.\n\"Fused Gromov-Wasserstein Graph Mixup for Graph-level Classifications\".\nIn Thirty-seventh Conference on Neural Information Processing Systems\n(NeurIPS), 2023.\n"
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‎master/_downloads/0e15d87ff8ae3d0dd037bf7ddc80d8a7/plot_variance.ipynb‎

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"\n# Sliced Wasserstein Distance on 2D distributions\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.8.0.</p></div>\n\nThis example illustrates the computation of the sliced Wasserstein Distance as\nproposed in [31].\n\n[31] Bonneel, Nicolas, et al. \"Sliced and radon wasserstein barycenters of\nmeasures.\" Journal of Mathematical Imaging and Vision 51.1 (2015): 22-45\n"
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"\n# Sliced Wasserstein Distance on 2D distributions\n\n<div class=\"alert alert-info\"><h4>Note</h4>\n\nExample added in release: 0.8.0.\n\n</div>\n\nThis example illustrates the computation of the sliced Wasserstein Distance as\nproposed in [31].\n\n[31] Bonneel, Nicolas, et al. \"Sliced and radon wasserstein barycenters of\nmeasures.\" Journal of Mathematical Imaging and Vision 51.1 (2015): 22-45\n"
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‎master/_downloads/0e77b32207676919c68b7f28c6029b1b/plot_unmix_optim_torch.ipynb‎

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"\n# Wasserstein unmixing with PyTorch\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.8.0.</p></div>\n\nIn this example we estimate mixing parameters from distributions that minimize\nthe Wasserstein distance. In other words we suppose that a target\ndistribution $\\mu^t$ can be expressed as a weighted sum of source\ndistributions $\\mu^s_k$ with the following model:\n\n\\begin{align}\\mu^t = \\sum_{k=1}^K w_k\\mu^s_k\\end{align}\n\nwhere $\\mathbf{w}$ is a vector of size $K$ and belongs in the\ndistribution simplex $\\Delta_K$.\n\nIn order to estimate this weight vector we propose to optimize the Wasserstein\ndistance between the model and the observed $\\mu^t$ with respect to\nthe vector. This leads to the following optimization problem:\n\n\\begin{align}\\min_{\\mathbf{w}\\in\\Delta_K} \\quad W \\left(\\mu^t,\\sum_{k=1}^K w_k\\mu^s_k\\right)\\end{align}\n\nThis minimization is done in this example with a simple projected gradient\ndescent in PyTorch. We use the automatic backend of POT that allows us to\ncompute the Wasserstein distance with :any:`ot.emd2` with\ndifferentiable losses.\n"
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"\n# Wasserstein unmixing with PyTorch\n\n<div class=\"alert alert-info\"><h4>Note</h4>\n\nExample added in release: 0.8.0.\n\n</div>\n\nIn this example we estimate mixing parameters from distributions that minimize\nthe Wasserstein distance. In other words we suppose that a target\ndistribution $\\mu^t$ can be expressed as a weighted sum of source\ndistributions $\\mu^s_k$ with the following model:\n\n\\begin{align}\\mu^t = \\sum_{k=1}^K w_k\\mu^s_k\\end{align}\n\nwhere $\\mathbf{w}$ is a vector of size $K$ and belongs in the\ndistribution simplex $\\Delta_K$.\n\nIn order to estimate this weight vector we propose to optimize the Wasserstein\ndistance between the model and the observed $\\mu^t$ with respect to\nthe vector. This leads to the following optimization problem:\n\n\\begin{align}\\min_{\\mathbf{w}\\in\\Delta_K} \\quad W \\left(\\mu^t,\\sum_{k=1}^K w_k\\mu^s_k\\right)\\end{align}\n\nThis minimization is done in this example with a simple projected gradient\ndescent in PyTorch. We use the automatic backend of POT that allows us to\ncompute the Wasserstein distance with :any:`ot.emd2` with\ndifferentiable losses.\n"
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‎master/_downloads/0eb518a5cb2af5a1870fc1f120d1483e/plot_partial_wass_and_gromov.ipynb‎

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"\n# Partial Wasserstein and Gromov-Wasserstein example\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.7.0.</p></div>\n\nThis example is designed to show how to use the Partial (Gromov-)Wasserstein\ndistance computation in POT [29].\n\n[29] Chapel, L., Alaya, M., Gasso, G. (2020). \"Partial Optimal\nTransport with Applications on Positive-Unlabeled Learning\". NeurIPS.\n"
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"\n# Partial Wasserstein and Gromov-Wasserstein example\n\n<div class=\"alert alert-info\"><h4>Note</h4>\n\nExample added in release: 0.7.0.\n\n</div>\n\nThis example is designed to show how to use the Partial (Gromov-)Wasserstein\ndistance computation in POT [29].\n\n[29] Chapel, L., Alaya, M., Gasso, G. (2020). \"Partial Optimal\nTransport with Applications on Positive-Unlabeled Learning\". NeurIPS.\n"
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