content: #!/usr/bin/python
  # -*- coding: utf-8 -*-
  """
  =========================================================
  Importance of Feature Scaling
  =========================================================
  
  Feature scaling though standardization (or Z-score normalization)
  can be an important preprocessing step for many machine learning
  algorithms. Standardization involves rescaling the features such
  that they have the properties of a standard normal distribution
  with a mean of zero and a standard deviation of one.
  
  While many algorithms (such as SVM, K-nearest neighbors, and logistic
  regression) require features to be normalized, intuitively we can
  think of Principle Component Analysis (PCA) as being a prime example
  of when normalization is important. In PCA we are interested in the
  components that maximize the variance. If one component (e.g. human
  height) varies less than another (e.g. weight) because of their
  respective scales (meters vs. kilos), PCA might determine that the
  direction of maximal variance more closely corresponds with the
  'weight' axis, if those features are not scaled. As a change in
  height of one meter can be considered much more important than the
  change in weight of one kilogram, this is clearly incorrect.
  
  To illustrate this, PCA is performed comparing the use of data with
  :class:`StandardScaler <sklearn.preprocessing.StandardScaler>` applied,
  to unscaled data. The results are visualized and a clear difference noted.
  The 1st principal component in the unscaled set can be seen. It can be seen
  that feature #13 dominates the direction, being a whole two orders of
  magnitude above the other features. This is contrasted when observing
  the principal component for the scaled version of the data. In the scaled
  version, the orders of magnitude are roughly the same across all the features.
  
  The dataset used is the Wine Dataset available at UCI. This dataset
  has continuous features that are heterogeneous in scale due to differing
  properties that they measure (i.e alcohol content, and malic acid).
  
  The transformed data is then used to train a naive Bayes classifier, and a
  clear difference in prediction accuracies is observed wherein the dataset
  which is scaled before PCA vastly outperforms the unscaled version.
  
  """
  from __future__ import print_function
  from sklearn.model_selection import train_test_split
  from sklearn.preprocessing import StandardScaler
  from sklearn.decomposition import PCA
  from sklearn.naive_bayes import GaussianNB
  from sklearn import metrics
  import matplotlib.pyplot as plt
  from sklearn.datasets import load_wine
  from sklearn.pipeline import make_pipeline
  print(__doc__)
  
  # Code source: Tyler Lanigan <tylerlanigan@gmail.com>
  #              Sebastian Raschka <mail@sebastianraschka.com>
  
  # License: BSD 3 clause
  
  RANDOM_STATE = 42
  FIG_SIZE = (10, 7)
  
  
  features, target = load_wine(return_X_y=True)
  
  # Make a train/test split using 30% test size
  X_train, X_test, y_train, y_test = train_test_split(features, target,
                                                      test_size=0.30,
                                                      random_state=RANDOM_STATE)
  
  # Fit to data and predict using pipelined GNB and PCA.
  unscaled_clf = make_pipeline(PCA(n_components=2), GaussianNB())
  unscaled_clf.fit(X_train, y_train)
  pred_test = unscaled_clf.predict(X_test)
  
  # Fit to data and predict using pipelined scaling, GNB and PCA.
  std_clf = make_pipeline(StandardScaler(), PCA(n_components=2), GaussianNB())
  std_clf.fit(X_train, y_train)
  pred_test_std = std_clf.predict(X_test)
  
  # Show prediction accuracies in scaled and unscaled data.
  print('\nPrediction accuracy for the normal test dataset with PCA')
  print('{:.2%}\n'.format(metrics.accuracy_score(y_test, pred_test)))
  
  print('\nPrediction accuracy for the standardized test dataset with PCA')
  print('{:.2%}\n'.format(metrics.accuracy_score(y_test, pred_test_std)))
  
  # Extract PCA from pipeline
  pca = unscaled_clf.named_steps['pca']
  pca_std = std_clf.named_steps['pca']
  
  # Show first principal componenets
  print('\nPC 1 without scaling:\n', pca.components_[0])
  print('\nPC 1 with scaling:\n', pca_std.components_[0])
  
  # Scale and use PCA on X_train data for visualization.
  scaler = std_clf.named_steps['standardscaler']
  X_train_std = pca_std.transform(scaler.transform(X_train))
  
  # visualize standardized vs. untouched dataset with PCA performed
  fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=FIG_SIZE)
  
  
  for l, c, m in zip(range(0, 3), ('blue', 'red', 'green'), ('^', 's', 'o')):
      ax1.scatter(X_train[y_train == l, 0], X_train[y_train == l, 1],
                  color=c,
                  label='class %s' % l,
                  alpha=0.5,
                  marker=m
                  )
  
  for l, c, m in zip(range(0, 3), ('blue', 'red', 'green'), ('^', 's', 'o')):
      ax2.scatter(X_train_std[y_train == l, 0], X_train_std[y_train == l, 1],
                  color=c,
                  label='class %s' % l,
                  alpha=0.5,
                  marker=m
                  )
  
  ax1.set_title('Training dataset after PCA')
  ax2.set_title('Standardized training dataset after PCA')
  
  for ax in (ax1, ax2):
      ax.set_xlabel('1st principal component')
      ax.set_ylabel('2nd principal component')
      ax.legend(loc='upper right')
      ax.grid()
  
  plt.tight_layout()
  
  plt.show()
  