.. _sphx_glr__auto_examples_sinkhorn_multiscale:

.. _sinkhorn-multiscale:

The multiscale Sinkhorn algorithm
-------------------------------------

**Outperform** the baseline Auction and Sinkhorn algorithms
by a factor **x50-100** with adaptive coarse-to-fine strategies:


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    <div class="sphx-glr-thumbnails">


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    <div class="sphx-glr-thumbcontainer" tooltip="Dating back to the work of Schrödinger  - see e.g. (Léonard, 2013) for a modern review - entrop...">

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  .. image:: /_auto_examples/sinkhorn_multiscale/images/thumb/sphx_glr_plot_epsilon_scaling_thumb.png
    :alt:

  :ref:`sphx_glr__auto_examples_sinkhorn_multiscale_plot_epsilon_scaling.py`

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      <div class="sphx-glr-thumbnail-title">1) Blur parameter, scaling strategy</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In the previous notebook, we&#x27;ve seen that simulated annealing could be used to define efficient...">

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  .. image:: /_auto_examples/sinkhorn_multiscale/images/thumb/sphx_glr_plot_kernel_truncation_thumb.png
    :alt:

  :ref:`sphx_glr__auto_examples_sinkhorn_multiscale_plot_kernel_truncation.py`

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      <div class="sphx-glr-thumbnail-title">2) Kernel truncation, log-linear runtimes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Let&#x27;s use a custom clustering scheme to generalize the multiscale Sinkhorn algorithm to high-di...">

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  .. image:: /_auto_examples/sinkhorn_multiscale/images/thumb/sphx_glr_plot_optimal_transport_cluster_thumb.png
    :alt:

  :ref:`sphx_glr__auto_examples_sinkhorn_multiscale_plot_optimal_transport_cluster.py`

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      <div class="sphx-glr-thumbnail-title">3) Optimal Transport in high dimension</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Sinkhorn divergences rely on a simple idea: by blurring the transport plan through the addition...">

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  .. image:: /_auto_examples/sinkhorn_multiscale/images/thumb/sphx_glr_plot_transport_blur_thumb.png
    :alt:

  :ref:`sphx_glr__auto_examples_sinkhorn_multiscale_plot_transport_blur.py`

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      <div class="sphx-glr-thumbnail-title">4) Sinkhorn vs. blurred Wasserstein distances</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /_auto_examples/sinkhorn_multiscale/plot_epsilon_scaling
   /_auto_examples/sinkhorn_multiscale/plot_kernel_truncation
   /_auto_examples/sinkhorn_multiscale/plot_optimal_transport_cluster
   /_auto_examples/sinkhorn_multiscale/plot_transport_blur