content: """
  =================================
  Gaussian Mixture Model Ellipsoids
  =================================
  
  Plot the confidence ellipsoids of a mixture of two Gaussians with EM
  and variational Dirichlet process.
  
  Both models have access to five components with which to fit the
  data. Note that the EM model will necessarily use all five components
  while the DP model will effectively only use as many as are needed for
  a good fit. This is a property of the Dirichlet Process prior. Here we
  can see that the EM model splits some components arbitrarily, because it
  is trying to fit too many components, while the Dirichlet Process model
  adapts it number of state automatically.
  
  This example doesn't show it, as we're in a low-dimensional space, but
  another advantage of the Dirichlet process model is that it can fit
  full covariance matrices effectively even when there are less examples
  per cluster than there are dimensions in the data, due to
  regularization properties of the inference algorithm.
  """
  import itertools
  
  import numpy as np
  from scipy import linalg
  import matplotlib.pyplot as plt
  import matplotlib as mpl
  
  from sklearn import mixture
  
  # Number of samples per component
  n_samples = 500
  
  # Generate random sample, two components
  np.random.seed(0)
  C = np.array([[0., -0.1], [1.7, .4]])
  X = np.r_[np.dot(np.random.randn(n_samples, 2), C),
            .7 * np.random.randn(n_samples, 2) + np.array([-6, 3])]
  
  # Fit a mixture of Gaussians with EM using five components
  gmm = mixture.GMM(n_components=5, covariance_type='full')
  gmm.fit(X)
  
  # Fit a Dirichlet process mixture of Gaussians using five components
  dpgmm = mixture.DPGMM(n_components=5, covariance_type='full')
  dpgmm.fit(X)
  
  color_iter = itertools.cycle(['r', 'g', 'b', 'c', 'm'])
  
  for i, (clf, title) in enumerate([(gmm, 'GMM'),
                                    (dpgmm, 'Dirichlet Process GMM')]):
      splot = plt.subplot(2, 1, 1 + i)
      Y_ = clf.predict(X)
      for i, (mean, covar, color) in enumerate(zip(
              clf.means_, clf._get_covars(), color_iter)):
          v, w = linalg.eigh(covar)
          u = w[0] / linalg.norm(w[0])
          # as the DP will not use every component it has access to
          # unless it needs it, we shouldn't plot the redundant
          # components.
          if not np.any(Y_ == i):
              continue
          plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], .8, color=color)
  
          # Plot an ellipse to show the Gaussian component
          angle = np.arctan(u[1] / u[0])
          angle = 180 * angle / np.pi  # convert to degrees
          ell = mpl.patches.Ellipse(mean, v[0], v[1], 180 + angle, color=color)
          ell.set_clip_box(splot.bbox)
          ell.set_alpha(0.5)
          splot.add_artist(ell)
  
      plt.xlim(-10, 10)
      plt.ylim(-3, 6)
      plt.xticks(())
      plt.yticks(())
      plt.title(title)
  
  plt.show()
  