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

.. only:: html

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

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

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

.. _sphx_glr_examples_pcovc_PCovC_Comparison.py:


Comparing PCovC with PCA and LDA
================================

.. GENERATED FROM PYTHON SOURCE LINES 10-27

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    from sklearn.datasets import load_breast_cancer
    from sklearn.decomposition import PCA
    from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
    from sklearn.linear_model import LogisticRegressionCV
    from sklearn.preprocessing import StandardScaler

    from skmatter.decomposition import PCovC


    plt.rcParams["image.cmap"] = "tab10"
    plt.rcParams["scatter.edgecolors"] = "k"

    random_state = 0








.. GENERATED FROM PYTHON SOURCE LINES 28-30

For this, we will use the :func:`sklearn.datasets.load_breast_cancer` dataset from
``sklearn``.

.. GENERATED FROM PYTHON SOURCE LINES 31-37

.. code-block:: Python


    X, y = load_breast_cancer(return_X_y=True)

    scaler = StandardScaler()
    X_scaled = scaler.fit_transform(X)








.. GENERATED FROM PYTHON SOURCE LINES 38-41

PCA
---


.. GENERATED FROM PYTHON SOURCE LINES 42-58

.. code-block:: Python


    pca = PCA(n_components=2)

    pca.fit(X_scaled, y)
    T_pca = pca.transform(X_scaled)

    fig, ax = plt.subplots()
    scatter = ax.scatter(T_pca[:, 0], T_pca[:, 1], c=y)
    ax.set(xlabel="PC$_1$", ylabel="PC$_2$")
    ax.legend(
        scatter.legend_elements()[0][::-1],
        load_breast_cancer().target_names[::-1],
        loc="upper right",
        title="Classes",
    )




.. image-sg:: /examples/pcovc/images/sphx_glr_PCovC_Comparison_001.png
   :alt: PCovC Comparison
   :srcset: /examples/pcovc/images/sphx_glr_PCovC_Comparison_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7ee561f79810>



.. GENERATED FROM PYTHON SOURCE LINES 59-62

LDA
---


.. GENERATED FROM PYTHON SOURCE LINES 63-73

.. code-block:: Python


    lda = LinearDiscriminantAnalysis(n_components=1)
    lda.fit(X_scaled, y)

    T_lda = lda.transform(X_scaled)

    fig, ax = plt.subplots()
    ax.scatter(T_lda[:], np.zeros(len(T_lda[:])), c=y)
    ax.set(xlabel="LDA$_1$", ylabel="LDA$_2$")




.. image-sg:: /examples/pcovc/images/sphx_glr_PCovC_Comparison_002.png
   :alt: PCovC Comparison
   :srcset: /examples/pcovc/images/sphx_glr_PCovC_Comparison_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    [Text(0.5, 23.52222222222222, 'LDA$_1$'), Text(22.472222222222214, 0.5, 'LDA$_2$')]



.. GENERATED FROM PYTHON SOURCE LINES 74-80

PCovC
-------------------

Below, we see the map produced
by a PCovC model with :math:`\alpha` = 0.5 and a logistic
regression classifier.

.. GENERATED FROM PYTHON SOURCE LINES 81-98

.. code-block:: Python


    mixing = 0.5

    pcovc = PCovC(
        mixing=mixing,
        n_components=2,
        random_state=random_state,
        classifier=LogisticRegressionCV(),
    )
    pcovc.fit(X_scaled, y)

    T_pcovc = pcovc.transform(X_scaled)

    fig, ax = plt.subplots()
    ax.scatter(T_pcovc[:, 0], T_pcovc[:, 1], c=y)
    ax.set(xlabel="PCov$_1$", ylabel="PCov$_2$")




.. image-sg:: /examples/pcovc/images/sphx_glr_PCovC_Comparison_003.png
   :alt: PCovC Comparison
   :srcset: /examples/pcovc/images/sphx_glr_PCovC_Comparison_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    [Text(0.5, 23.52222222222222, 'PCov$_1$'), Text(44.347222222222214, 0.5, 'PCov$_2$')]



.. GENERATED FROM PYTHON SOURCE LINES 99-101

A side-by-side comparison of the
three maps (PCA, LDA, and PCovC):

.. GENERATED FROM PYTHON SOURCE LINES 102-113

.. code-block:: Python


    fig, axs = plt.subplots(1, 3, figsize=(18, 5))
    axs[0].scatter(T_pca[:, 0], T_pca[:, 1], c=y)
    axs[0].set_title("PCA")
    axs[1].scatter(T_lda, np.zeros(len(T_lda)), c=y)
    axs[1].set_title("LDA")
    axs[2].scatter(T_pcovc[:, 0], T_pcovc[:, 1], c=y)
    axs[2].set_title("PCovC")

    plt.tight_layout()
    plt.show()



.. image-sg:: /examples/pcovc/images/sphx_glr_PCovC_Comparison_004.png
   :alt: PCA, LDA, PCovC
   :srcset: /examples/pcovc/images/sphx_glr_PCovC_Comparison_004.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_examples_pcovc_PCovC_Comparison.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_