.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/decomposition/plot_varimax_fa.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_decomposition_plot_varimax_fa.py>`
        to download the full example code or to run this example in your browser via JupyterLite or Binder

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

.. _sphx_glr_auto_examples_decomposition_plot_varimax_fa.py:


===============================================================
Factor Analysis (with rotation) to visualize patterns
===============================================================

Investigating the Iris dataset, we see that sepal length, petal
length and petal width are highly correlated. Sepal width is
less redundant. Matrix decomposition techniques can uncover
these latent patterns. Applying rotations to the resulting
components does not inherently improve the predictive value
of the derived latent space, but can help visualise their
structure; here, for example, the varimax rotation, which
is found by maximizing the squared variances of the weights,
finds a structure where the second component only loads
positively on sepal width.

.. GENERATED FROM PYTHON SOURCE LINES 18-29

.. code-block:: Python


    # Authors: Jona Sassenhagen
    # License: BSD 3 clause

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import load_iris
    from sklearn.decomposition import PCA, FactorAnalysis
    from sklearn.preprocessing import StandardScaler








.. GENERATED FROM PYTHON SOURCE LINES 30-31

Load Iris data

.. GENERATED FROM PYTHON SOURCE LINES 31-35

.. code-block:: Python

    data = load_iris()
    X = StandardScaler().fit_transform(data["data"])
    feature_names = data["feature_names"]








.. GENERATED FROM PYTHON SOURCE LINES 36-37

Plot covariance of Iris features

.. GENERATED FROM PYTHON SOURCE LINES 37-50

.. code-block:: Python

    ax = plt.axes()

    im = ax.imshow(np.corrcoef(X.T), cmap="RdBu_r", vmin=-1, vmax=1)

    ax.set_xticks([0, 1, 2, 3])
    ax.set_xticklabels(list(feature_names), rotation=90)
    ax.set_yticks([0, 1, 2, 3])
    ax.set_yticklabels(list(feature_names))

    plt.colorbar(im).ax.set_ylabel("$r$", rotation=0)
    ax.set_title("Iris feature correlation matrix")
    plt.tight_layout()




.. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_001.png
   :alt: Iris feature correlation matrix
   :srcset: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 51-52

Run factor analysis with Varimax rotation

.. GENERATED FROM PYTHON SOURCE LINES 52-79

.. code-block:: Python

    n_comps = 2

    methods = [
        ("PCA", PCA()),
        ("Unrotated FA", FactorAnalysis()),
        ("Varimax FA", FactorAnalysis(rotation="varimax")),
    ]
    fig, axes = plt.subplots(ncols=len(methods), figsize=(10, 8), sharey=True)

    for ax, (method, fa) in zip(axes, methods):
        fa.set_params(n_components=n_comps)
        fa.fit(X)

        components = fa.components_.T
        print("\n\n %s :\n" % method)
        print(components)

        vmax = np.abs(components).max()
        ax.imshow(components, cmap="RdBu_r", vmax=vmax, vmin=-vmax)
        ax.set_yticks(np.arange(len(feature_names)))
        ax.set_yticklabels(feature_names)
        ax.set_title(str(method))
        ax.set_xticks([0, 1])
        ax.set_xticklabels(["Comp. 1", "Comp. 2"])
    fig.suptitle("Factors")
    plt.tight_layout()
    plt.show()



.. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_002.png
   :alt: Factors, PCA, Unrotated FA, Varimax FA
   :srcset: /auto_examples/decomposition/images/sphx_glr_plot_varimax_fa_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none



     PCA :

    [[ 0.52106591  0.37741762]
     [-0.26934744  0.92329566]
     [ 0.5804131   0.02449161]
     [ 0.56485654  0.06694199]]


     Unrotated FA :

    [[ 0.88096009 -0.4472869 ]
     [-0.41691605 -0.55390036]
     [ 0.99918858  0.01915283]
     [ 0.96228895  0.05840206]]


     Varimax FA :

    [[ 0.98633022 -0.05752333]
     [-0.16052385 -0.67443065]
     [ 0.90809432  0.41726413]
     [ 0.85857475  0.43847489]]





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

   **Total running time of the script:** (0 minutes 0.355 seconds)


.. _sphx_glr_download_auto_examples_decomposition_plot_varimax_fa.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/decomposition/plot_varimax_fa.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/decomposition/plot_varimax_fa.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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


.. include:: plot_varimax_fa.recommendations


.. only:: html

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

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