content: """
  =========================================================
  Comparing different clustering algorithms on toy datasets
  =========================================================
  
  This example shows characteristics of different
  clustering algorithms on datasets that are "interesting"
  but still in 2D. With the exception of the last dataset,
  the parameters of each of these dataset-algorithm pairs
  has been tuned to produce good clustering results. Some
  algorithms are more sensitive to parameter values than
  others.
  
  The last dataset is an example of a 'null' situation for
  clustering: the data is homogeneous, and there is no good
  clustering. For this example, the null dataset uses the
  same parameters as the dataset in the row above it, which
  represents a mismatch in the parameter values and the
  data structure.
  
  While these examples give some intuition about the
  algorithms, this intuition might not apply to very high
  dimensional data.
  """
  print(__doc__)
  
  import time
  import warnings
  
  import numpy as np
  import matplotlib.pyplot as plt
  
  from sklearn import cluster, datasets, mixture
  from sklearn.neighbors import kneighbors_graph
  from sklearn.preprocessing import StandardScaler
  from itertools import cycle, islice
  
  np.random.seed(0)
  
  # ============
  # Generate datasets. We choose the size big enough to see the scalability
  # of the algorithms, but not too big to avoid too long running times
  # ============
  n_samples = 1500
  noisy_circles = datasets.make_circles(n_samples=n_samples, factor=.5,
                                        noise=.05)
  noisy_moons = datasets.make_moons(n_samples=n_samples, noise=.05)
  blobs = datasets.make_blobs(n_samples=n_samples, random_state=8)
  no_structure = np.random.rand(n_samples, 2), None
  
  # Anisotropicly distributed data
  random_state = 170
  X, y = datasets.make_blobs(n_samples=n_samples, random_state=random_state)
  transformation = [[0.6, -0.6], [-0.4, 0.8]]
  X_aniso = np.dot(X, transformation)
  aniso = (X_aniso, y)
  
  # blobs with varied variances
  varied = datasets.make_blobs(n_samples=n_samples,
                               cluster_std=[1.0, 2.5, 0.5],
                               random_state=random_state)
  
  # ============
  # Set up cluster parameters
  # ============
  plt.figure(figsize=(9 * 2 + 3, 12.5))
  plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
                      hspace=.01)
  
  plot_num = 1
  
  default_base = {'quantile': .3,
                  'eps': .3,
                  'damping': .9,
                  'preference': -200,
                  'n_neighbors': 10,
                  'n_clusters': 3}
  
  datasets = [
      (noisy_circles, {'damping': .77, 'preference': -240,
                       'quantile': .2, 'n_clusters': 2}),
      (noisy_moons, {'damping': .75, 'preference': -220, 'n_clusters': 2}),
      (varied, {'eps': .18, 'n_neighbors': 2}),
      (aniso, {'eps': .15, 'n_neighbors': 2}),
      (blobs, {}),
      (no_structure, {})]
  
  for i_dataset, (dataset, algo_params) in enumerate(datasets):
      # update parameters with dataset-specific values
      params = default_base.copy()
      params.update(algo_params)
  
      X, y = dataset
  
      # normalize dataset for easier parameter selection
      X = StandardScaler().fit_transform(X)
  
      # estimate bandwidth for mean shift
      bandwidth = cluster.estimate_bandwidth(X, quantile=params['quantile'])
  
      # connectivity matrix for structured Ward
      connectivity = kneighbors_graph(
          X, n_neighbors=params['n_neighbors'], include_self=False)
      # make connectivity symmetric
      connectivity = 0.5 * (connectivity + connectivity.T)
  
      # ============
      # Create cluster objects
      # ============
      ms = cluster.MeanShift(bandwidth=bandwidth, bin_seeding=True)
      two_means = cluster.MiniBatchKMeans(n_clusters=params['n_clusters'])
      ward = cluster.AgglomerativeClustering(
          n_clusters=params['n_clusters'], linkage='ward',
          connectivity=connectivity)
      spectral = cluster.SpectralClustering(
          n_clusters=params['n_clusters'], eigen_solver='arpack',
          affinity="nearest_neighbors")
      dbscan = cluster.DBSCAN(eps=params['eps'])
      affinity_propagation = cluster.AffinityPropagation(
          damping=params['damping'], preference=params['preference'])
      average_linkage = cluster.AgglomerativeClustering(
          linkage="average", affinity="cityblock",
          n_clusters=params['n_clusters'], connectivity=connectivity)
      birch = cluster.Birch(n_clusters=params['n_clusters'])
      gmm = mixture.GaussianMixture(
          n_components=params['n_clusters'], covariance_type='full')
  
      clustering_algorithms = (
          ('MiniBatchKMeans', two_means),
          ('AffinityPropagation', affinity_propagation),
          ('MeanShift', ms),
          ('SpectralClustering', spectral),
          ('Ward', ward),
          ('AgglomerativeClustering', average_linkage),
          ('DBSCAN', dbscan),
          ('Birch', birch),
          ('GaussianMixture', gmm)
      )
  
      for name, algorithm in clustering_algorithms:
          t0 = time.time()
  
          # catch warnings related to kneighbors_graph
          with warnings.catch_warnings():
              warnings.filterwarnings(
                  "ignore",
                  message="the number of connected components of the " +
                  "connectivity matrix is [0-9]{1,2}" +
                  " > 1. Completing it to avoid stopping the tree early.",
                  category=UserWarning)
              warnings.filterwarnings(
                  "ignore",
                  message="Graph is not fully connected, spectral embedding" +
                  " may not work as expected.",
                  category=UserWarning)
              algorithm.fit(X)
  
          t1 = time.time()
          if hasattr(algorithm, 'labels_'):
              y_pred = algorithm.labels_.astype(np.int)
          else:
              y_pred = algorithm.predict(X)
  
          plt.subplot(len(datasets), len(clustering_algorithms), plot_num)
          if i_dataset == 0:
              plt.title(name, size=18)
  
          colors = np.array(list(islice(cycle(['#377eb8', '#ff7f00', '#4daf4a',
                                               '#f781bf', '#a65628', '#984ea3',
                                               '#999999', '#e41a1c', '#dede00']),
                                        int(max(y_pred) + 1))))
          plt.scatter(X[:, 0], X[:, 1], s=10, color=colors[y_pred])
  
          plt.xlim(-2.5, 2.5)
          plt.ylim(-2.5, 2.5)
          plt.xticks(())
          plt.yticks(())
          plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'),
                   transform=plt.gca().transAxes, size=15,
                   horizontalalignment='right')
          plot_num += 1
  
  plt.show()
  