old_contents: """
  ===============================
  Plot classification probability
  ===============================
  """
  # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  # License: BSD Style.
  
  # $Id$
  
  import pylab as pl
  import numpy as np
  
  from scikits.learn.logistic import LogisticRegression
  from scikits.learn.svm import SVC
  from scikits.learn import datasets
  
  iris = datasets.load_iris()
  X = iris.data[:, :2] # we only take the first two features for visualization
  y = iris.target
  
  n_features = X.shape[1]
  
  C = 1.0
  
  # Create classifier (any of the following 3)
  classifier = LogisticRegression(C=C, penalty='l1')
  classifier = LogisticRegression(C=C, penalty='l2')
  classifier = SVC(kernel='linear', C=C, probability=True)
  
  classifier.fit(X, y)
  
  y_pred = classifier.predict(X)
  classif_rate = np.mean(y_pred.ravel() == y.ravel()) * 100
  print  "classif_rate : %f " % classif_rate
  
  # ======================
  # = View probabilities =
  # ======================
  pl.figure()
  xx = np.linspace(3,9,100)
  yy = np.linspace(1,5,100).T
  xx, yy = np.meshgrid(xx, yy)
  Xfull = np.c_[xx.ravel(),yy.ravel()]
  probas = classifier.predict_proba(Xfull)
  n_classes = np.unique(y_pred).size
  for k in range(n_classes):
      pl.subplot(1, n_classes, k + 1)
      pl.title("Class %d" % k)
      imshow_handle = pl.imshow(probas[:,k].reshape((100, 100)), extent=(3, 9, 1, 5), origin='lower')
      pl.hold(True)
      idx = (y_pred == k)
      if idx.any(): pl.scatter(X[idx,0], X[idx,1], marker='o', c='k')
  
  ax = pl.axes([0.15,0.04,0.7,0.05])
  pl.title("Probability")
  pl.colorbar(imshow_handle, cax=ax, orientation='horizontal')
  
  pl.show()
  
new_contents: """
  ===============================
  Plot classification probability
  ===============================
  
  Plot the classification probability for different classifiers. We use a 3
  class dataset, and we classify it with a Support Vector classifier, as
  well as L1 and L2 penalized logistic regression.
  
  The logistic regression is not a multiclass classifier out of the box. As
  a result it can identify only the first class.
  """
  # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  # License: BSD Style.
  
  # $Id$
  
  import pylab as pl
  import numpy as np
  
  from scikits.learn.logistic import LogisticRegression
  from scikits.learn.svm import SVC
  from scikits.learn import datasets
  
  iris = datasets.load_iris()
  X = iris.data[:, :2] # we only take the first two features for visualization
  y = iris.target
  
  n_features = X.shape[1]
  
  C = 1.0
  
  # Create different classifiers. The logistic regression cannot do
  # multiclass out of the box.
  classifiers = {
                  'L1 logistic': LogisticRegression(C=C, penalty='l1'),
                  'L2 logistic': LogisticRegression(C=C, penalty='l2'),
                  'Linear SVC': SVC(kernel='linear', C=C, probability=True),
                }
  
  n_classifiers = len(classifiers)
  
  pl.figure(figsize=(3*2, n_classifiers*2))
  pl.subplots_adjust(bottom=.2, top=.95)
  
  for index, (name, classifier) in enumerate(classifiers.iteritems()):
      classifier.fit(X, y)
  
      y_pred = classifier.predict(X)
      classif_rate = np.mean(y_pred.ravel() == y.ravel()) * 100
      print  "classif_rate for %s : %f " % (name, classif_rate)
  
      # View probabilities=
      xx = np.linspace(3,9,100)
      yy = np.linspace(1,5,100).T
      xx, yy = np.meshgrid(xx, yy)
      Xfull = np.c_[xx.ravel(),yy.ravel()]
      probas = classifier.predict_proba(Xfull)
      n_classes = np.unique(y_pred).size
      for k in range(n_classes):
          pl.subplot(n_classifiers, n_classes, index*n_classes + k + 1)
          pl.title("Class %d" % k)
          if k == 0:
              pl.ylabel(name)
          imshow_handle = pl.imshow(probas[:, k].reshape((100, 100)), 
                                    extent=(3, 9, 1, 5), origin='lower')
          pl.xticks(())
          pl.yticks(())
          idx = (y_pred == k)
          if idx.any(): 
              pl.scatter(X[idx, 0], X[idx, 1], marker='o', c='k')
  
  ax = pl.axes([0.15, 0.04, 0.7, 0.05])
  pl.title("Probability")
  pl.colorbar(imshow_handle, cax=ax, orientation='horizontal')
  
  pl.show()
  
subject: Enhance plot_classification_probability example.