content: """
  ====================================
  Demonstration of k-means assumptions
  ====================================
  
  This example is meant to illustrate situations where k-means will produce
  unintuitive and possibly unexpected clusters. In the first three plots, the
  input data does not conform to some implicit assumption that k-means makes and
  undesirable clusters are produced as a result. In the last plot, k-means
  returns intuitive clusters despite unevenly sized blobs.
  """
  print(__doc__)
  
  # Author: Phil Roth <mr.phil.roth@gmail.com>
  # License: BSD 3 clause
  
  import numpy as np
  import matplotlib.pyplot as plt
  
  from sklearn.cluster import KMeans
  from sklearn.datasets import make_blobs
  
  plt.figure(figsize=(12, 12))
  
  n_samples = 1500
  random_state = 170
  X, y = make_blobs(n_samples=n_samples, random_state=random_state)
  
  # Incorrect number of clusters
  y_pred = KMeans(n_clusters=2, random_state=random_state).fit_predict(X)
  
  plt.subplot(221)
  plt.scatter(X[:, 0], X[:, 1], c=y_pred)
  plt.title("Incorrect Number of Blobs")
  
  # Anisotropicly distributed data
  transformation = [[ 0.60834549, -0.63667341], [-0.40887718, 0.85253229]]
  X_aniso = np.dot(X, transformation)
  y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)
  
  plt.subplot(222)
  plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred)
  plt.title("Anisotropicly Distributed Blobs")
  
  # Different variance
  X_varied, y_varied = make_blobs(n_samples=n_samples,
                                  cluster_std=[1.0, 2.5, 0.5],
                                  random_state=random_state)
  y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)
  
  plt.subplot(223)
  plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred)
  plt.title("Unequal Variance")
  
  # Unevenly sized blobs
  X_filtered = np.vstack((X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]))
  y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_filtered)
  
  plt.subplot(224)
  plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred)
  plt.title("Unevenly Sized Blobs")
  
  plt.show()
  