.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/neighbors/plot_kde_1d.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_neighbors_plot_kde_1d.py: =================================== 简单的一维核密度估计 =================================== 本示例使用 :class:`~sklearn.neighbors.KernelDensity` 类来演示一维核密度估计的原理。 第一个图展示了使用直方图来可视化一维点密度的问题之一。直观上，直方图可以被认为是一种在规则网格上每个点上方堆叠一个单位“块”的方案。然而，如顶部两个面板所示，这些块的网格选择可能导致对密度分布的潜在形状产生截然不同的看法。如果我们将每个块中心放在它所代表的点上，我们会得到左下角面板中显示的估计。这是一种使用“平顶”核的核密度估计。这一思想可以推广到其他核形状：第一幅图的右下角面板显示了相同分布上的高斯核密度估计。 Scikit-learn 通过 :class:`~sklearn.neighbors.KernelDensity` 估计器实现了使用球树或 KD 树结构的高效核密度估计。可用的核在本示例的第二幅图中显示。 第三幅图比较了一维分布中100个样本的核密度估计。尽管本示例使用的是一维分布，但核密度估计可以轻松且高效地扩展到更高维度。 .. GENERATED FROM PYTHON SOURCE LINES 14-142 .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_kde_1d_001.png :alt: plot kde 1d :srcset: /auto_examples/neighbors/images/sphx_glr_plot_kde_1d_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_kde_1d_002.png :alt: Available Kernels :srcset: /auto_examples/neighbors/images/sphx_glr_plot_kde_1d_002.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_kde_1d_003.png :alt: plot kde 1d :srcset: /auto_examples/neighbors/images/sphx_glr_plot_kde_1d_003.png :class: sphx-glr-multi-img .. code-block:: Python # Author: Jake Vanderplas # import matplotlib.pyplot as plt import numpy as np from scipy.stats import norm from sklearn.neighbors import KernelDensity # ---------------------------------------------------------------------- # 绘制直方图到核密度估计的演变过程 np.random.seed(1) N = 20 X = np.concatenate( (np.random.normal(0, 1, int(0.3 * N)), np.random.normal(5, 1, int(0.7 * N))) )[:, np.newaxis] X_plot = np.linspace(-5, 10, 1000)[:, np.newaxis] bins = np.linspace(-5, 10, 10) fig, ax = plt.subplots(2, 2, sharex=True, sharey=True) fig.subplots_adjust(hspace=0.05, wspace=0.05) # histogram 1 ax[0, 0].hist(X[:, 0], bins=bins, fc="#AAAAFF", density=True) ax[0, 0].text(-3.5, 0.31, "Histogram") # histogram 2 ax[0, 1].hist(X[:, 0], bins=bins + 0.75, fc="#AAAAFF", density=True) ax[0, 1].text(-3.5, 0.31, "Histogram, bins shifted") # tophat KDE kde = KernelDensity(kernel="tophat", bandwidth=0.75).fit(X) log_dens = kde.score_samples(X_plot) ax[1, 0].fill(X_plot[:, 0], np.exp(log_dens), fc="#AAAAFF") ax[1, 0].text(-3.5, 0.31, "Tophat Kernel Density") # 高斯核密度估计（KDE） kde = KernelDensity(kernel="gaussian", bandwidth=0.75).fit(X) log_dens = kde.score_samples(X_plot) ax[1, 1].fill(X_plot[:, 0], np.exp(log_dens), fc="#AAAAFF") ax[1, 1].text(-3.5, 0.31, "Gaussian Kernel Density") for axi in ax.ravel(): axi.plot(X[:, 0], np.full(X.shape[0], -0.01), "+k") axi.set_xlim(-4, 9) axi.set_ylim(-0.02, 0.34) for axi in ax[:, 0]: axi.set_ylabel("Normalized Density") for axi in ax[1, :]: axi.set_xlabel("x") # ---------------------------------------------------------------------- # 绘制所有可用的核函数 X_plot = np.linspace(-6, 6, 1000)[:, None] X_src = np.zeros((1, 1)) fig, ax = plt.subplots(2, 3, sharex=True, sharey=True) fig.subplots_adjust(left=0.05, right=0.95, hspace=0.05, wspace=0.05) def format_func(x, loc): if x == 0: return "0" elif x == 1: return "h" elif x == -1: return "-h" else: return "%ih" % x for i, kernel in enumerate( ["gaussian", "tophat", "epanechnikov", "exponential", "linear", "cosine"] ): axi = ax.ravel()[i] log_dens = KernelDensity(kernel=kernel).fit(X_src).score_samples(X_plot) axi.fill(X_plot[:, 0], np.exp(log_dens), "-k", fc="#AAAAFF") axi.text(-2.6, 0.95, kernel) axi.xaxis.set_major_formatter(plt.FuncFormatter(format_func)) axi.xaxis.set_major_locator(plt.MultipleLocator(1)) axi.yaxis.set_major_locator(plt.NullLocator()) axi.set_ylim(0, 1.05) axi.set_xlim(-2.9, 2.9) ax[0, 1].set_title("Available Kernels") # ---------------------------------------------------------------------- # 绘制一维密度示例 N = 100 np.random.seed(1) X = np.concatenate( (np.random.normal(0, 1, int(0.3 * N)), np.random.normal(5, 1, int(0.7 * N))) )[:, np.newaxis] X_plot = np.linspace(-5, 10, 1000)[:, np.newaxis] true_dens = 0.3 * norm(0, 1).pdf(X_plot[:, 0]) + 0.7 * norm(5, 1).pdf(X_plot[:, 0]) fig, ax = plt.subplots() ax.fill(X_plot[:, 0], true_dens, fc="black", alpha=0.2, label="input distribution") colors = ["navy", "cornflowerblue", "darkorange"] kernels = ["gaussian", "tophat", "epanechnikov"] lw = 2 for color, kernel in zip(colors, kernels): kde = KernelDensity(kernel=kernel, bandwidth=0.5).fit(X) log_dens = kde.score_samples(X_plot) ax.plot( X_plot[:, 0], np.exp(log_dens), color=color, lw=lw, linestyle="-", label="kernel = '{0}'".format(kernel), ) ax.text(6, 0.38, "N={0} points".format(N)) ax.legend(loc="upper left") ax.plot(X[:, 0], -0.005 - 0.01 * np.random.random(X.shape[0]), "+k") ax.set_xlim(-4, 9) ax.set_ylim(-0.02, 0.4) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.265 seconds) .. _sphx_glr_download_auto_examples_neighbors_plot_kde_1d.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/neighbors/plot_kde_1d.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_kde_1d.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_kde_1d.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_kde_1d.zip ` .. include:: plot_kde_1d.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_