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+
+
+.. _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
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_