.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/basics/demo_pca_via_affinity_matcher.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_basics_demo_pca_via_affinity_matcher.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_basics_demo_pca_via_affinity_matcher.py:


PCA via SVD and via AffinityMatcher
===================================

We show how to compute a PCA embedding using the closed form
and using the AffinityMatcher class. Both approaches lead to the same solution.

.. GENERATED FROM PYTHON SOURCE LINES 9-20

.. code-block:: Python


    # Author: Hugues Van Assel <vanasselhugues@gmail.com>
    #
    # License: BSD 3-Clause License

    import matplotlib.pyplot as plt
    from sklearn.datasets import load_digits

    from torchdr import AffinityMatcher, ScalarProductAffinity
    from torchdr.spectral import PCA








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Load toy images
---------------

First, let's load 5 classes of the digits dataset from sklearn.

.. GENERATED FROM PYTHON SOURCE LINES 25-30

.. code-block:: Python


    digits = load_digits(n_class=5)
    X = digits.data
    X = X - X.mean(0)








.. GENERATED FROM PYTHON SOURCE LINES 31-37

PCA via SVD
-----------

Let us perform PCA using the closed form solution given by the
Singular Value Decomposition (SVD).
In ``Torchdr``, it is available at :class:`torchdr.PCA`.

.. GENERATED FROM PYTHON SOURCE LINES 37-46

.. code-block:: Python


    Z_svd = PCA(n_components=2).fit_transform(X)

    plt.figure()
    plt.scatter(Z_svd[:, 0], Z_svd[:, 1], c=digits.target)
    plt.title("PCA via SVD")
    plt.show()





.. image-sg:: /auto_examples/basics/images/sphx_glr_demo_pca_via_affinity_matcher_001.png
   :alt: PCA via SVD
   :srcset: /auto_examples/basics/images/sphx_glr_demo_pca_via_affinity_matcher_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 47-56

PCA via AffinityMatcher
-----------------------

Now, let us perform PCA using the AffinityMatcher class
:class:`torchdr.AffinityMatcher`
as well as the scalar product affinity
:class:`torchdr.ScalarProductAffinity`
for both input data and embeddings,
and the square loss as global objective.

.. GENERATED FROM PYTHON SOURCE LINES 56-75

.. code-block:: Python


    model = AffinityMatcher(
        n_components=2,
        affinity_in=ScalarProductAffinity(),
        affinity_out=ScalarProductAffinity(),
        loss_fn="square_loss",
        init="normal",
        lr=1e1,
        max_iter=50,
        backend=None,
    )
    Z_am = model.fit_transform(X)

    plt.figure()
    plt.scatter(Z_am[:, 0], Z_am[:, 1], c=digits.target)
    plt.title("PCA via AffinityMatcher")
    plt.show()





.. image-sg:: /auto_examples/basics/images/sphx_glr_demo_pca_via_affinity_matcher_002.png
   :alt: PCA via AffinityMatcher
   :srcset: /auto_examples/basics/images/sphx_glr_demo_pca_via_affinity_matcher_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 76-78

We can see that we obtain the same PCA embedding (up to a rotation) using
both methods.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 4.218 seconds)


.. _sphx_glr_download_auto_examples_basics_demo_pca_via_affinity_matcher.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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

    .. container:: sphx-glr-download sphx-glr-download-python

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: demo_pca_via_affinity_matcher.zip <demo_pca_via_affinity_matcher.zip>`


.. only:: html

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

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