.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/cluster/plot_kmeans_assumptions.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_cluster_plot_kmeans_assumptions.py: ==================================== k-means 假设的演示 ==================================== 此示例旨在说明 k-means 产生非直观且可能不理想的聚类的情况。 .. GENERATED FROM PYTHON SOURCE LINES 9-13 .. code-block:: Python # 作者：scikit-learn 开发者 # SPDX 许可证标识符：BSD-3-Clause .. GENERATED FROM PYTHON SOURCE LINES 14-18 数据生成 --------------- 函数 :func:`~sklearn.datasets.make_blobs` 生成各向同性（球形）的高斯斑点。要获得各向异性（椭圆形）的高斯斑点，需要定义一个线性 `变换` 。 .. GENERATED FROM PYTHON SOURCE LINES 18-37 .. code-block:: Python import numpy as np from sklearn.datasets import make_blobs n_samples = 1500 random_state = 170 transformation = [[0.60834549, -0.63667341], [-0.40887718, 0.85253229]] X, y = make_blobs(n_samples=n_samples, random_state=random_state) X_aniso = np.dot(X, transformation) # Anisotropic blobs X_varied, y_varied = make_blobs( n_samples=n_samples, cluster_std=[1.0, 2.5, 0.5], random_state=random_state ) # Unequal variance X_filtered = np.vstack( (X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]) ) # Unevenly sized blobs y_filtered = [0] * 500 + [1] * 100 + [2] * 10 .. GENERATED FROM PYTHON SOURCE LINES 38-39 我们可以将结果数据可视化： .. GENERATED FROM PYTHON SOURCE LINES 39-60 .. code-block:: Python import matplotlib.pyplot as plt fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(12, 12)) axs[0, 0].scatter(X[:, 0], X[:, 1], c=y) axs[0, 0].set_title("Mixture of Gaussian Blobs") axs[0, 1].scatter(X_aniso[:, 0], X_aniso[:, 1], c=y) axs[0, 1].set_title("Anisotropically Distributed Blobs") axs[1, 0].scatter(X_varied[:, 0], X_varied[:, 1], c=y_varied) axs[1, 0].set_title("Unequal Variance") axs[1, 1].scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_filtered) axs[1, 1].set_title("Unevenly Sized Blobs") plt.suptitle("Ground truth clusters").set_y(0.95) plt.show() .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_001.png :alt: Ground truth clusters, Mixture of Gaussian Blobs, Anisotropically Distributed Blobs, Unequal Variance, Unevenly Sized Blobs :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 61-70 拟合模型并绘制结果 --------------------------- 之前生成的数据现在用于展示 :class:`~sklearn.cluster.KMeans` 在以下场景中的表现： - 非最优的聚类数量：在实际情况下，没有唯一定义的 **真正** 聚类数量。适当的聚类数量需要根据数据标准和预期目标来决定。 - 各向异性分布的斑点：k-means通过最小化样本到其分配的聚类中心的欧几里得距离来工作。因此，k-means更适用于各向同性且正态分布的聚类（即球形高斯分布）。 - 不同的方差：k-means等价于对具有相同方差但均值可能不同的k个高斯分布的“混合”进行最大似然估计。 - 不均匀大小的斑点：没有关于k-means的理论结果表明它需要相似的聚类大小才能表现良好，但最小化欧几里得距离意味着问题越稀疏且维度越高，就越需要使用不同的聚类中心种子运行算法以确保全局最小惯性。 .. GENERATED FROM PYTHON SOURCE LINES 70-99 .. code-block:: Python from sklearn.cluster import KMeans common_params = { "n_init": "auto", "random_state": random_state, } fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(12, 12)) y_pred = KMeans(n_clusters=2, **common_params).fit_predict(X) axs[0, 0].scatter(X[:, 0], X[:, 1], c=y_pred) axs[0, 0].set_title("Non-optimal Number of Clusters") y_pred = KMeans(n_clusters=3, **common_params).fit_predict(X_aniso) axs[0, 1].scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred) axs[0, 1].set_title("Anisotropically Distributed Blobs") y_pred = KMeans(n_clusters=3, **common_params).fit_predict(X_varied) axs[1, 0].scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred) axs[1, 0].set_title("Unequal Variance") y_pred = KMeans(n_clusters=3, **common_params).fit_predict(X_filtered) axs[1, 1].scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred) axs[1, 1].set_title("Unevenly Sized Blobs") plt.suptitle("Unexpected KMeans clusters").set_y(0.95) plt.show() .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_002.png :alt: Unexpected KMeans clusters, Non-optimal Number of Clusters, Anisotropically Distributed Blobs, Unequal Variance, Unevenly Sized Blobs :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 100-106 可能的解决方案 ------------------ 要了解如何找到正确的簇数量，请参见 :ref:`sphx_glr_auto_examples_cluster_plot_kmeans_silhouette_analysis.py` 。 在这种情况下，将 `n_clusters` 设置为 3 即可。 .. GENERATED FROM PYTHON SOURCE LINES 106-112 .. code-block:: Python y_pred = KMeans(n_clusters=3, **common_params).fit_predict(X) plt.scatter(X[:, 0], X[:, 1], c=y_pred) plt.title("Optimal Number of Clusters") plt.show() .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_003.png :alt: Optimal Number of Clusters :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 113-114 为了处理大小不均匀的斑点，可以增加随机初始化的次数。在这种情况下，我们设置 `n_init=10` 以避免找到次优的局部最小值。更多细节请参见 :ref:`kmeans_sparse_high_dim` 。 .. GENERATED FROM PYTHON SOURCE LINES 114-123 .. code-block:: Python y_pred = KMeans(n_clusters=3, n_init=10, random_state=random_state).fit_predict( X_filtered ) plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred) plt.title("Unevenly Sized Blobs \nwith several initializations") plt.show() .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_004.png :alt: Unevenly Sized Blobs with several initializations :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 124-128 由于各向异性和不等方差是 k-means 算法的实际限制，这里我们建议使用 :class:`~sklearn.mixture.GaussianMixture` ，它同样假设高斯簇，但不对其方差施加任何约束。请注意，仍然需要找到正确的簇数（参见 :ref:`sphx_glr_auto_examples_mixture_plot_gmm_selection.py` ）。 关于其他聚类方法如何处理各向异性或不等方差的簇的示例，请参见示例 :ref:`sphx_glr_auto_examples_cluster_plot_cluster_comparison.py` 。 .. GENERATED FROM PYTHON SOURCE LINES 128-144 .. code-block:: Python from sklearn.mixture import GaussianMixture fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 6)) y_pred = GaussianMixture(n_components=3).fit_predict(X_aniso) ax1.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred) ax1.set_title("Anisotropically Distributed Blobs") y_pred = GaussianMixture(n_components=3).fit_predict(X_varied) ax2.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred) ax2.set_title("Unequal Variance") plt.suptitle("Gaussian mixture clusters").set_y(0.95) plt.show() .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_005.png :alt: Gaussian mixture clusters, Anisotropically Distributed Blobs, Unequal Variance :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 145-151 最终备注 ------------- 在高维空间中，欧几里得距离往往会变得膨胀（在此示例中未显示）。在进行k-means聚类之前运行降维算法可以缓解这个问题并加快计算速度（参见示例 :ref:`sphx_glr_auto_examples_text_plot_document_clustering.py` ）。 在已知簇是各向同性、具有相似方差且不太稀疏的情况下，k-means 算法非常有效，并且是现有最快的聚类算法之一。如果必须多次重新启动以避免收敛到局部最小值，这一优势将丧失。 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.539 seconds) .. _sphx_glr_download_auto_examples_cluster_plot_kmeans_assumptions.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/cluster/plot_kmeans_assumptions.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_kmeans_assumptions.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_kmeans_assumptions.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_kmeans_assumptions.zip ` .. include:: plot_kmeans_assumptions.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_