.. _sphx_glr_auto_examples_plot_WDA.py:


=================================
Wasserstein Discriminant Analysis
=================================

This example illustrate the use of WDA as proposed in [11].


[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016).
Wasserstein Discriminant Analysis.




.. code-block:: python


    # Author: Remi Flamary <remi.flamary@unice.fr>
    #
    # License: MIT License

    import numpy as np
    import matplotlib.pylab as pl

    from ot.dr import wda, fda








Generate data
-------------



.. code-block:: python


    #%% parameters

    n = 1000  # nb samples in source and target datasets
    nz = 0.2

    # generate circle dataset
    t = np.random.rand(n) * 2 * np.pi
    ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1
    xs = np.concatenate(
        (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)
    xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2)

    t = np.random.rand(n) * 2 * np.pi
    yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1
    xt = np.concatenate(
        (np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)
    xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2)

    nbnoise = 8

    xs = np.hstack((xs, np.random.randn(n, nbnoise)))
    xt = np.hstack((xt, np.random.randn(n, nbnoise)))







Plot data
---------



.. code-block:: python


    #%% plot samples
    pl.figure(1, figsize=(6.4, 3.5))

    pl.subplot(1, 2, 1)
    pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker='+', label='Source samples')
    pl.legend(loc=0)
    pl.title('Discriminant dimensions')

    pl.subplot(1, 2, 2)
    pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker='+', label='Source samples')
    pl.legend(loc=0)
    pl.title('Other dimensions')
    pl.tight_layout()




.. image:: /auto_examples/images/sphx_glr_plot_WDA_001.png
    :align: center




Compute Fisher Discriminant Analysis
------------------------------------



.. code-block:: python


    #%% Compute FDA
    p = 2

    Pfda, projfda = fda(xs, ys, p)







Compute Wasserstein Discriminant Analysis
-----------------------------------------



.. code-block:: python


    #%% Compute WDA
    p = 2
    reg = 1e0
    k = 10
    maxiter = 100

    Pwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter)






.. rst-class:: sphx-glr-script-out

 Out::

    Compiling cost function...
    Computing gradient of cost function...
     iter              cost val         grad. norm
        1   +9.0167295050534191e-01 2.28422652e-01
        2   +4.8324990550878105e-01 4.89362707e-01
        3   +3.4613154515357075e-01 2.84117562e-01
        4   +2.5277108387195002e-01 1.24888750e-01
        5   +2.4113858393736629e-01 8.07491482e-02
        6   +2.3642108593032782e-01 1.67612140e-02
        7   +2.3625721372202199e-01 7.68640008e-03
        8   +2.3625461994913738e-01 7.42200784e-03
        9   +2.3624493441436939e-01 6.43534105e-03
       10   +2.3621901383686217e-01 2.17960585e-03
       11   +2.3621854258326572e-01 2.03306749e-03
       12   +2.3621696458678049e-01 1.37118721e-03
       13   +2.3621569489873540e-01 2.76368907e-04
       14   +2.3621565599232983e-01 1.41898134e-04
       15   +2.3621564465487518e-01 5.96602069e-05
       16   +2.3621564232556647e-01 1.08709521e-05
       17   +2.3621564230277003e-01 9.17855656e-06
       18   +2.3621564224857586e-01 1.73728345e-06
       19   +2.3621564224748123e-01 1.17770019e-06
       20   +2.3621564224658587e-01 2.16179383e-07
    Terminated - min grad norm reached after 20 iterations, 9.20 seconds.


Plot 2D projections
-------------------



.. code-block:: python


    #%% plot samples

    xsp = projfda(xs)
    xtp = projfda(xt)

    xspw = projwda(xs)
    xtpw = projwda(xt)

    pl.figure(2)

    pl.subplot(2, 2, 1)
    pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples')
    pl.legend(loc=0)
    pl.title('Projected training samples FDA')

    pl.subplot(2, 2, 2)
    pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples')
    pl.legend(loc=0)
    pl.title('Projected test samples FDA')

    pl.subplot(2, 2, 3)
    pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples')
    pl.legend(loc=0)
    pl.title('Projected training samples WDA')

    pl.subplot(2, 2, 4)
    pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples')
    pl.legend(loc=0)
    pl.title('Projected test samples WDA')
    pl.tight_layout()

    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_WDA_003.png
    :align: center




**Total running time of the script:** ( 0 minutes  16.182 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_WDA.py <plot_WDA.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_WDA.ipynb <plot_WDA.ipynb>`

.. rst-class:: sphx-glr-signature

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