8000 Add new example for plotting a confidence_ellipse · matplotlib/matplotlib@9661375 · GitHub
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Commit 9661375

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Carsten
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Add new example for plotting a confidence_ellipse
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‎examples/statistics/confidence_ellipse.py

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"""
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======================================================
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Plot a confidence ellipse of a two-dimensional dataset
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======================================================
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This example shows how to plot a confidence ellipse of a
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two-dimensional dataset, using its pearson correlation coefficient.
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The approach that is used to obtain the correct geometry is
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explained and proved here:
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https://carstenschelp.github.io/2018/09/14/Plot_Confidence_Ellipse_001.html
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.patches import Ellipse
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import matplotlib.transforms as transforms
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def confidence_ellipse(x, y, ax, n_std=3.0, **kwargs):
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"""
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Create a plot of the covariance confidence ellipse of `x` and `y`
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Parameters
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----------
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x, y : array_like, shape (n, )
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Input data
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ax : matplotlib.axes object to the ellipse into
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n_std : number of standard deviations to determine the ellipse's radiuses
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Returns
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-------
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None
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Other parameters
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----------------
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kwargs : `~matplotlib.patches.Patch` properties
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author : Carsten Schelp
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license: GNU General Public License v3.0 (https://github.com/CarstenSchelp/CarstenSchelp.github.io/blob/master/LICENSE)
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"""
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if x.size != y.size:
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raise ValueError("x and y must be the same size")
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cov = np.cov(x, y)
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pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1,1])
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# Using a special case to obtain the eigenvalues of this two-dimensionl dataset.
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ell_radius_x = np.sqrt(1 + pearson)
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ell_radius_y = np.sqrt(1 - pearson)
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ellipse = Ellipse((0,0), width=ell_radius_x * 2, height=ell_radius_y * 2, **kwargs)
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# Calculating the stdandard deviation of x from the squareroot of the variance
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# and multiplying with the given number of standard deviations.
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scale_x = np.sqrt(cov[0, 0]) * n_std
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mean_x = np.mean(x)
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# calculating the stdandard deviation of y ...
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scale_y = np.sqrt(cov[1, 1]) * n_std
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mean_y = np.mean(y)
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transf = transforms.Affine2D() \
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.rotate_deg(45) \
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.scale(scale_x, scale_y) \
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.translate(mean_x, mean_y)
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ellipse.set_transform(transf + ax.transData)
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ax.add_patch(ellipse)
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def get_correlated_dataset(n, dependency, mu, scale):
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latent = np.random.randn(n, 2)
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dependent = latent.dot(dependency)
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scaled = dependent * scale
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scaled_with_offset = scaled + mu
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# return x and y of the new, correlated dataset
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return scaled_with_offset[:,0],scaled_with_offset[:,1]
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fig, ((ax_pos, ax_neg, ax_uncorrel), (ax_nstd1, ax_nstd2, ax_kwargs)) = plt.subplots(nrows=2, ncols=3, figsize=(9, 6), sharex=True, sharey=True)
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np.random.seed(1234)
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# Demo top left: positive correlation
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# Create a matrix that transforms the independent "latent" dataset
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# into a dataset where x and y are correlated - positive correlation, in this case.
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dependency_pos = np.array([
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[0.85, 0.35],
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[0.15, -0.65]
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])
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mu_pos = np.array([2, 4]).T
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scale_pos = np.array([3, 5]).T
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# Indicate the x- and y-axis
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ax_pos.axvline(c='grey', lw=1)
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ax_pos.axhline(c='grey', lw=1)
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x, y = get_correlated_dataset(500, dependency_pos, mu_pos, scale_pos)
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confidence_ellipse(x, y, ax_pos, facecolor='none', edgecolor='red')
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# Also plot the dataset itself, for reference
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ax_pos.scatter(x, y, s=0.5)
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# Mark the mean ("mu")
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ax_pos.scatter([mu_pos[0]], [mu_pos[1]],c='red', s=3)
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ax_pos.set_title(f'Positive correlation')
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# Demo top middle: negative correlation
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dependency_neg = np.array([
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[0.9, -0.4],
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[0.1, -0.6]
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])
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mu = np.array([2, 4]).T
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scale = np.array([3, 5]).T
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# Indicate the x- and y-axes
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ax_neg.axvline(c='grey', lw=1)
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ax_neg.axhline(c='grey', lw=1)
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x, y = get_correlated_dataset(500, dependency_neg, mu, scale)
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confidence_ellipse(x, y, ax_neg, facecolor='none', edgecolor='red')
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# Again, plot the dataset itself, for reference
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ax_neg.scatter(x, y, s=0.5)
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# Mark the mean ("mu")
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ax_neg.scatter([mu[0]], [mu[1]],c='red', s=3)
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ax_neg.set_title(f'Negative correlation')
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# Demo top right: uncorrelated dataset
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# This uncorrelated plot (bottom left) is not a circle since x and y
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# are differently scaled. However, the fact that x and y are uncorrelated
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# is shown however by the ellipse being aligned with the x- and y-axis.
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in_dependency = np.array([
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[1, 0],
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[0, 1]
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])
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mu = np.array([2, 4]).T
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scale = np.array([5, 3]).T
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ax_uncorrel.axvline(c='grey', lw=1)
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ax_uncorrel.axhline(c='grey', lw=1)
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x, y = get_correlated_dataset(500, in_dependency, mu, scale)
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confidence_ellipse(x, y, ax_uncorrel, facecolor='none', edgecolor='red')
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ax_uncorrel.scatter(x, y, s=0.5)
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ax_uncorrel.scatter([mu[0]], [mu[1]],c='red', s=3)
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ax_uncorrel.set_title(f'Weak correlation')
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# Demo bottom left and middle: ellipse two standard deviations wide
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# In the confidence_ellipse function the default of the number
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# of standard deviations is 3, which makes the ellipse enclose
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# 99.7% of the points when the data is normally distributed.
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# This demo shows a two plots of the same dataset with different
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# values for "n_std".
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dependency_nstd_1 = np.array([
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[0.8, 0.75],
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[-0.2, 0.35]
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])
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mu = np.array([0, 0]).T
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scale = np.array([8, 5]).T
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ax_kwargs.axvline(c='grey', lw=1)
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ax_kwargs.axhline(c='grey', lw=1)
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x, y = get_correlated_dataset(500, dependency_nstd_1, mu, scale)
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# Onde standard deviation
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# Now plot the dataset first ("under" the ellipse) in order to
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# demonstrate the transparency of the ellipse (alpha).
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ax_nstd1.scatter(x, y, s=0.5)
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confidence_ellipse(x, y, ax_nstd1, n_std=1, facecolor='none', edgecolor='red')
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confidence_ellipse(x, y, ax_nstd1, n_std=3, facecolor='none', edgecolor='gray', linestyle='--')
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ax_nstd1.scatter([mu[0]], [mu[1]],c='red', s=3)
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ax_nstd1.set_title(f'One standard deviation')
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# Two standard deviations
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ax_nstd2.scatter(x, y, s=0.5)
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confidence_ellipse(x, y, ax_nstd2, n_std=2, facecolor='none', edgecolor='red')
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confidence_ellipse(x, y, ax_nstd2, n_std=3, facecolor='none', edgecolor='gray', linestyle='--')
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ax_nstd2.scatter([mu[0]], [mu[1]],c='red', s=3)
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ax_nstd2.set_title(f'Two standard deviations')
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# Demo bottom right: Using kwargs
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dependency_kwargs = np.array([
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[-0.8, 0.5],
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[-0.2, 0.5]
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])
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mu = np.array([2, -3]).T
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scale = np.array([6, 5]).T
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ax_kwargs.axvline(c='grey', lw=1)
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ax_kwargs.axhline(c='grey', lw=1)
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x, y = get_correlated_dataset(500, dependency_kwargs, mu, scale)
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# Now plot the dataset first ("under" the ellipse) in order to
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# demonstrate the transparency of the ellipse (alpha).
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ax_kwargs.scatter(x, y, s=0.5)
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confidence_ellipse(x, y, ax_kwargs, alpha=0.5, facecolor='pink', edgecolor='purple')
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ax_kwargs.scatter([mu[0]], [mu[1]],c='red', s=3)
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ax_kwargs.set_title(f'Using kwargs')
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fig.subplots_adjust(hspace=0.25)
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plt.show()

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