.. 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 Binder

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

.. _sphx_glr_auto_examples_decomposition_plot_varimax_fa.py:


===============================================================
因子分析（带旋转）以可视化模式
===============================================================

研究鸢尾花数据集，我们发现花萼长度、花瓣长度和花瓣宽度高度相关。花萼宽度的冗余性较低。矩阵分解技术可以揭示这些潜在模式。对结果组件应用旋转并不会本质上提高衍生潜在空间的预测价值，但可以帮助可视化它们的结构；例如，这里的方差最大化旋转，通过最大化权重的平方方差找到一种结构，其中第二个组件仅在花萼宽度上正加载。

.. GENERATED FROM PYTHON SOURCE LINES 9-20

.. code-block:: Python


    # 作者：scikit-learn 开发者
    # SPDX 许可证标识符：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 21-23

%%
加载鸢尾花数据

.. GENERATED FROM PYTHON SOURCE LINES 23-28

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 29-30

绘制鸢尾花特征的协方差

.. GENERATED FROM PYTHON SOURCE LINES 30-43

.. 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 44-45

进行带有方差最大化旋转的因子分析

.. GENERATED FROM PYTHON SOURCE LINES 45-73

.. 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 0.239 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:: 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>`

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

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


.. include:: plot_varimax_fa.recommendations


.. only:: html

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

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