content: """
  =====================
  SVM: Weighted samples
  =====================
  
  Plot decision function of a weighted dataset, where the size of points
  is proportional to its weight.
  
  The sample weighting rescales the C parameter, which means that the classifier
  puts more emphasis on getting these points right. The effect might often be
  subtle.
  To emphasize the effect here, we particularly weight outliers, making the
  deformation of the decision boundary very visible.
  """
  print(__doc__)
  
  import numpy as np
  import matplotlib.pyplot as plt
  from sklearn import svm
  
  
  def plot_decision_function(classifier, sample_weight, axis, title):
      # plot the decision function
      xx, yy = np.meshgrid(np.linspace(-4, 5, 500), np.linspace(-4, 5, 500))
  
      Z = classifier.decision_function(np.c_[xx.ravel(), yy.ravel()])
      Z = Z.reshape(xx.shape)
  
      # plot the line, the points, and the nearest vectors to the plane
      axis.contourf(xx, yy, Z, alpha=0.75, cmap=plt.cm.bone)
      axis.scatter(X[:, 0], X[:, 1], c=Y, s=100 * sample_weight, alpha=0.9,
                   cmap=plt.cm.bone)
  
      axis.axis('off')
      axis.set_title(title)
  
  
  # we create 20 points
  np.random.seed(0)
  X = np.r_[np.random.randn(10, 2) + [1, 1], np.random.randn(10, 2)]
  Y = [1] * 10 + [-1] * 10
  sample_weight_last_ten = abs(np.random.randn(len(X)))
  sample_weight_constant = np.ones(len(X))
  # and bigger weights to some outliers
  sample_weight_last_ten[15:] *= 5
  sample_weight_last_ten[9] *= 15
  
  # for reference, first fit without class weights
  
  # fit the model
  clf_weights = svm.SVC()
  clf_weights.fit(X, Y, sample_weight=sample_weight_last_ten)
  
  clf_no_weights = svm.SVC()
  clf_no_weights.fit(X, Y)
  
  fig, axes = plt.subplots(1, 2, figsize=(14, 6))
  plot_decision_function(clf_no_weights, sample_weight_constant, axes[0],
                         "Constant weights")
  plot_decision_function(clf_weights, sample_weight_last_ten, axes[1],
                         "Modified weights")
  
  plt.show()
  