.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/mixture/plot_gmm_selection.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` 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_selection.py: ================================ 高斯混合模型选择 ================================ 本示例展示了如何使用高斯混合模型（GMM）和 :ref:`信息论标准 ` 进行模型选择。模型选择涉及模型中的协方差类型和成分数量。 在这种情况下，赤池信息准则（AIC）和贝叶斯信息准则（BIC）都能提供正确的结果，但我们只演示后者，因为BIC更适合在一组候选模型中识别真实模型。与贝叶斯方法不同，这种推断是无先验的。 .. GENERATED FROM PYTHON SOURCE LINES 13-17 数据生成 --------------- 我们通过随机采样 `numpy.random.randn` 返回的标准正态分布生成两个组件（每个组件包含 `n_samples` ）。一个组件保持球形但进行了平移和重新缩放。另一个组件被变形以具有更一般的协方差矩阵。 .. GENERATED FROM PYTHON SOURCE LINES 17-28 .. code-block:: Python import numpy as np n_samples = 500 np.random.seed(0) C = np.array([[0.0, -0.1], [1.7, 0.4]]) component_1 = np.dot(np.random.randn(n_samples, 2), C) # general component_2 = 0.7 * np.random.randn(n_samples, 2) + np.array([-4, 1]) # spherical X = np.concatenate([component_1, component_2]) .. GENERATED FROM PYTHON SOURCE LINES 29-30 我们可以将不同的组件可视化： .. GENERATED FROM PYTHON SOURCE LINES 30-40 .. code-block:: Python import matplotlib.pyplot as plt plt.scatter(component_1[:, 0], component_1[:, 1], s=0.8) plt.scatter(component_2[:, 0], component_2[:, 1], s=0.8) plt.title("Gaussian Mixture components") plt.axis("equal") plt.show() .. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_001.png :alt: Gaussian Mixture components :srcset: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 41-54 模型训练与选择 ---------------------------- 我们将成分数量从1到6进行变化，并使用不同类型的协方差参数： - `"full"` ：每个成分都有自己的通用协方差矩阵。 - `"tied"` ：所有成分共享同一个通用协方差矩阵。 - `"diag"` ：每个成分都有自己的对角协方差矩阵。 - `"spherical"` ：每个成分都有自己的单一方差。 我们对不同的模型进行评分，并保留最佳模型（即BIC最低的模型）。这是通过使用 :class:`~sklearn.model_selection.GridSearchCV` 和一个用户定义的评分函数来实现的，该函数返回负的BIC分数，因为 :class:`~sklearn.model_selection.GridSearchCV` 旨在 **最大化** 一个分数（最大化负的BIC等同于最小化BIC）。 最佳参数集和估计器分别存储在 `best_parameters_` 和 `best_estimator_` 中。 .. GENERATED FROM PYTHON SOURCE LINES 54-74 .. code-block:: Python from sklearn.mixture import GaussianMixture from sklearn.model_selection import GridSearchCV def gmm_bic_score(estimator, X): """可传递给GridSearchCV以使用BIC评分的可调用对象。""" # 由于 GridSearchCV 期望最大化得分，因此将其取负。 return -estimator.bic(X) param_grid = { "n_components": range(1, 7), "covariance_type": ["spherical", "tied", "diag", "full"], } grid_search = GridSearchCV( GaussianMixture(), param_grid=param_grid, scoring=gmm_bic_score ) grid_search.fit(X) .. raw:: html 
GridSearchCV(estimator=GaussianMixture(),
                 param_grid={'covariance_type': ['spherical', 'tied', 'diag',
                                                 'full'],
                             'n_components': range(1, 7)},
                 scoring=<function gmm_bic_score at 0xffff4c10af20>)
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On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.


.. GENERATED FROM PYTHON SOURCE LINES 75-79 绘制BIC分数 ------------------- 为了简化绘图，我们可以从网格搜索交叉验证的结果中创建一个 `pandas.DataFrame` 。我们重新反转 BIC 分数的符号，以显示最小化它的效果。 .. GENERATED FROM PYTHON SOURCE LINES 79-95 .. code-block:: Python import pandas as pd df = pd.DataFrame(grid_search.cv_results_)[ ["param_n_components", "param_covariance_type", "mean_test_score"] ] df["mean_test_score"] = -df["mean_test_score"] df = df.rename( columns={ "param_n_components": "Number of components", "param_covariance_type": "Type of covariance", "mean_test_score": "BIC score", } ) df.sort_values(by="BIC score").head() .. raw:: html
Number of components Type of covariance BIC score
19 2 full 1046.829429
20 3 full 1084.038689
21 4 full 1114.517272
22 5 full 1148.512281
23 6 full 1179.977890


.. GENERATED FROM PYTHON SOURCE LINES 96-107 .. code-block:: Python import seaborn as sns sns.catplot( data=df, kind="bar", x="Number of components", y="BIC score", hue="Type of covariance", ) plt.show() .. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_002.png :alt: plot gmm selection :srcset: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 108-119 在当前情况下，具有2个成分和完整协方差的模型（对应于真实生成模型）具有最低的BIC分数，因此被网格搜索选中。 绘制最佳模型 ------------------- 我们绘制一个椭圆来展示所选模型的每个高斯分量。为此，需要找到由 `covariances_` 属性返回的协方差矩阵的特征值。这些矩阵的形状取决于 `covariance_type` ： - `"full"` ：( `n_components` , `n_features` , `n_features` ) - `"tied"` ：( `n_features` , `n_features` ) - `"diag"` ：( `n_components` , `n_features` ) - `"spherical"` ：( `n_components` ,) .. GENERATED FROM PYTHON SOURCE LINES 119-154 .. code-block:: Python from matplotlib.patches import Ellipse from scipy import linalg color_iter = sns.color_palette("tab10", 2)[::-1] Y_ = grid_search.predict(X) fig, ax = plt.subplots() for i, (mean, cov, color) in enumerate( zip( grid_search.best_estimator_.means_, grid_search.best_estimator_.covariances_, color_iter, ) ): v, w = linalg.eigh(cov) if not np.any(Y_ == i): continue plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], 0.8, color=color) angle = np.arctan2(w[0][1], w[0][0]) angle = 180.0 * angle / np.pi # convert to degrees v = 2.0 * np.sqrt(2.0) * np.sqrt(v) ellipse = Ellipse(mean, v[0], v[1], angle=180.0 + angle, color=color) ellipse.set_clip_box(fig.bbox) ellipse.set_alpha(0.5) ax.add_artist(ellipse) plt.title( f"Selected GMM: {grid_search.best_params_['covariance_type']} model, " f"{grid_search.best_params_['n_components']} components" ) plt.axis("equal") plt.show() .. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_003.png :alt: Selected GMM: full model, 2 components :srcset: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.737 seconds) .. _sphx_glr_download_auto_examples_mixture_plot_gmm_selection.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_selection.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_gmm_selection.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_gmm_selection.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_gmm_selection.zip ` .. include:: plot_gmm_selection.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_