content: """
  ====================================================================
  Normal and Shrinkage Linear Discriminant Analysis for classification
  ====================================================================
  
  Shows how shrinkage improves classification.
  """
  
  from __future__ import division
  
  import numpy as np
  import matplotlib.pyplot as plt
  
  from sklearn.datasets import make_blobs
  from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
  
  
  n_train = 20  # samples for training
  n_test = 200  # samples for testing
  n_averages = 50  # how often to repeat classification
  n_features_max = 75  # maximum number of features
  step = 4  # step size for the calculation
  
  
  def generate_data(n_samples, n_features):
      """Generate random blob-ish data with noisy features.
  
      This returns an array of input data with shape `(n_samples, n_features)`
      and an array of `n_samples` target labels.
  
      Only one feature contains discriminative information, the other features
      contain only noise.
      """
      X, y = make_blobs(n_samples=n_samples, n_features=1, centers=[[-2], [2]])
  
      # add non-discriminative features
      if n_features > 1:
          X = np.hstack([X, np.random.randn(n_samples, n_features - 1)])
      return X, y
  
  acc_clf1, acc_clf2 = [], []
  n_features_range = range(1, n_features_max + 1, step)
  for n_features in n_features_range:
      score_clf1, score_clf2 = 0, 0
      for _ in range(n_averages):
          X, y = generate_data(n_train, n_features)
  
          clf1 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage='auto').fit(X, y)
          clf2 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage=None).fit(X, y)
  
          X, y = generate_data(n_test, n_features)
          score_clf1 += clf1.score(X, y)
          score_clf2 += clf2.score(X, y)
  
      acc_clf1.append(score_clf1 / n_averages)
      acc_clf2.append(score_clf2 / n_averages)
  
  features_samples_ratio = np.array(n_features_range) / n_train
  
  plt.plot(features_samples_ratio, acc_clf1, linewidth=2,
           label="Linear Discriminant Analysis with shrinkage", color='r')
  plt.plot(features_samples_ratio, acc_clf2, linewidth=2,
           label="Linear Discriminant Analysis", color='g')
  
  plt.xlabel('n_features / n_samples')
  plt.ylabel('Classification accuracy')
  
  plt.legend(loc=1, prop={'size': 12})
  plt.suptitle('Linear Discriminant Analysis vs. \
  shrinkage Linear Discriminant Analysis (1 discriminative feature)')
  plt.show()
  