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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/mixture/plot_gmm_covariances.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_mixture_plot_gmm_covariances.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_mixture_plot_gmm_covariances.py:


===============
GMM 协方差
===============

高斯混合模型的几种协方差类型的演示。

有关估计器的更多信息，请参见 :ref:`gmm` 。

尽管 GMM 通常用于聚类，但我们可以将获得的聚类与数据集中的实际类别进行比较。我们用训练集中类别的均值初始化高斯分布的均值，以使这种比较有效。

我们使用鸢尾花数据集上的各种 GMM 协方差类型绘制训练数据和保留的测试数据上的预测标签。我们按性能递增顺序比较具有球形、对角线、完整和绑定协方差矩阵的 GMM。尽管一般来说完整协方差的表现最好，但它容易在小数据集上过拟合，并且不能很好地泛化到保留的测试数据。

在图中，训练数据显示为点，而测试数据显示为叉。鸢尾花数据集是四维的。这里只显示前两个维度，因此某些点在其他维度上是分开的。

.. GENERATED FROM PYTHON SOURCE LINES 17-125



.. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_gmm_covariances_001.png
   :alt: spherical, diag, tied, full
   :srcset: /auto_examples/mixture/images/sphx_glr_plot_gmm_covariances_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    # 作者：scikit-learn 开发者
    # SPDX-License-Identifier: BSD-3-Clause

    import matplotlib as mpl
    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn import datasets
    from sklearn.mixture import GaussianMixture
    from sklearn.model_selection import StratifiedKFold

    colors = ["navy", "turquoise", "darkorange"]


    def make_ellipses(gmm, ax):
        for n, color in enumerate(colors):
            if gmm.covariance_type == "full":
                covariances = gmm.covariances_[n][:2, :2]
            elif gmm.covariance_type == "tied":
                covariances = gmm.covariances_[:2, :2]
            elif gmm.covariance_type == "diag":
                covariances = np.diag(gmm.covariances_[n][:2])
            elif gmm.covariance_type == "spherical":
                covariances = np.eye(gmm.means_.shape[1]) * gmm.covariances_[n]
            v, w = np.linalg.eigh(covariances)
            u = w[0] / np.linalg.norm(w[0])
            angle = np.arctan2(u[1], u[0])
            angle = 180 * angle / np.pi  # convert to degrees
            v = 2.0 * np.sqrt(2.0) * np.sqrt(v)
            ell = mpl.patches.Ellipse(
                gmm.means_[n, :2], v[0], v[1], angle=180 + angle, color=color
            )
            ell.set_clip_box(ax.bbox)
            ell.set_alpha(0.5)
            ax.add_artist(ell)
            ax.set_aspect("equal", "datalim")


    iris = datasets.load_iris()

    # 将数据集划分为互不重叠的训练集（75%）和测试集（25%）。
    skf = StratifiedKFold(n_splits=4)
    # 只取第一折。
    train_index, test_index = next(iter(skf.split(iris.data, iris.target)))


    X_train = iris.data[train_index]
    y_train = iris.target[train_index]
    X_test = iris.data[test_index]
    y_test = iris.target[test_index]

    n_classes = len(np.unique(y_train))

    # 尝试使用不同类型的协方差矩阵进行高斯混合模型（GMM）分析。
    estimators = {
        cov_type: GaussianMixture(
            n_components=n_classes, covariance_type=cov_type, max_iter=20, random_state=0
        )
        for cov_type in ["spherical", "diag", "tied", "full"]
    }

    n_estimators = len(estimators)

    plt.figure(figsize=(3 * n_estimators // 2, 6))
    plt.subplots_adjust(
        bottom=0.01, top=0.95, hspace=0.15, wspace=0.05, left=0.01, right=0.99
    )


    for index, (name, estimator) in enumerate(estimators.items()):
        # 由于我们有训练数据的类别标签，我们可以以监督的方式初始化GMM参数。
        estimator.means_init = np.array(
            [X_train[y_train == i].mean(axis=0) for i in range(n_classes)]
        )

        # 使用EM算法训练其他参数。
        estimator.fit(X_train)

        h = plt.subplot(2, n_estimators // 2, index + 1)
        make_ellipses(estimator, h)

        for n, color in enumerate(colors):
            data = iris.data[iris.target == n]
            plt.scatter(
                data[:, 0], data[:, 1], s=0.8, color=color, label=iris.target_names[n]
            )
        # 用叉号绘制测试数据
        for n, color in enumerate(colors):
            data = X_test[y_test == n]
            plt.scatter(data[:, 0], data[:, 1], marker="x", color=color)

        y_train_pred = estimator.predict(X_train)
        train_accuracy = np.mean(y_train_pred.ravel() == y_train.ravel()) * 100
        plt.text(0.05, 0.9, "Train accuracy: %.1f" % train_accuracy, transform=h.transAxes)

        y_test_pred = estimator.predict(X_test)
        test_accuracy = np.mean(y_test_pred.ravel() == y_test.ravel()) * 100
        plt.text(0.05, 0.8, "Test accuracy: %.1f" % test_accuracy, transform=h.transAxes)

        plt.xticks(())
        plt.yticks(())
        plt.title(name)

    plt.legend(scatterpoints=1, loc="lower right", prop=dict(size=12))


    plt.show()


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

   **Total running time of the script:** (0 minutes 0.117 seconds)


.. _sphx_glr_download_auto_examples_mixture_plot_gmm_covariances.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/mixture/plot_gmm_covariances.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_gmm_covariances.recommendations


.. only:: html

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

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