content: """
  =================================
  Gaussian Mixture Model Selection
  =================================
  
  This example shows that model selection can be performed with
  Gaussian Mixture Models using information-theoretic criteria (BIC).
  Model selection concerns both the covariance type
  and the number of components in the model.
  In that case, AIC also provides the right result (not shown to save time),
  but BIC is better suited if the problem is to identify the right model.
  Unlike Bayesian procedures, such inferences are prior-free.
  
  In that case, the model with 2 components and full covariance
  (which corresponds to the true generative model) is selected.
  """
  print(__doc__)
  
  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])]
  
  lowest_bic = np.infty
  bic = []
  n_components_range = range(1, 7)
  cv_types = ['spherical', 'tied', 'diag', 'full']
  for cv_type in cv_types:
      for n_components in n_components_range:
          # Fit a mixture of Gaussians with EM
          gmm = mixture.GMM(n_components=n_components, covariance_type=cv_type)
          gmm.fit(X)
          bic.append(gmm.bic(X))
          if bic[-1] < lowest_bic:
              lowest_bic = bic[-1]
              best_gmm = gmm
  
  bic = np.array(bic)
  color_iter = itertools.cycle(['k', 'r', 'g', 'b', 'c', 'm', 'y'])
  clf = best_gmm
  bars = []
  
  # Plot the BIC scores
  spl = plt.subplot(2, 1, 1)
  for i, (cv_type, color) in enumerate(zip(cv_types, color_iter)):
      xpos = np.array(n_components_range) + .2 * (i - 2)
      bars.append(plt.bar(xpos, bic[i * len(n_components_range):
                                    (i + 1) * len(n_components_range)],
                          width=.2, color=color))
  plt.xticks(n_components_range)
  plt.ylim([bic.min() * 1.01 - .01 * bic.max(), bic.max()])
  plt.title('BIC score per model')
  xpos = np.mod(bic.argmin(), len(n_components_range)) + .65 +\
      .2 * np.floor(bic.argmin() / len(n_components_range))
  plt.text(xpos, bic.min() * 0.97 + .03 * bic.max(), '*', fontsize=14)
  spl.set_xlabel('Number of components')
  spl.legend([b[0] for b in bars], cv_types)
  
  # Plot the winner
  splot = plt.subplot(2, 1, 2)
  Y_ = clf.predict(X)
  for i, (mean, covar, color) in enumerate(zip(clf.means_, clf.covars_,
                                               color_iter)):
      v, w = linalg.eigh(covar)
      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.arctan2(w[0][1], w[0][0])
      angle = 180 * angle / np.pi  # convert to degrees
      v *= 4
      ell = mpl.patches.Ellipse(mean, v[0], v[1], 180 + angle, color=color)
      ell.set_clip_box(splot.bbox)
      ell.set_alpha(.5)
      splot.add_artist(ell)
  
  plt.xlim(-10, 10)
  plt.ylim(-3, 6)
  plt.xticks(())
  plt.yticks(())
  plt.title('Selected GMM: full model, 2 components')
  plt.subplots_adjust(hspace=.35, bottom=.02)
  plt.show()
  