content: """
  =================================================
  Hyper-parameters of Approximate Nearest Neighbors
  =================================================
  
  This example demonstrates the behaviour of the
  accuracy of the nearest neighbor queries of Locality Sensitive Hashing
  Forest as the number of candidates and the number of estimators (trees)
  vary.
  
  In the first plot, accuracy is measured with the number of candidates. Here,
  the term "number of candidates" refers to maximum bound for the number of
  distinct points retrieved from each tree to calculate the distances. Nearest
  neighbors are selected from this pool of candidates. Number of estimators is
  maintained at three fixed levels (1, 5, 10).
  
  In the second plot, the number of candidates is fixed at 50. Number of trees
  is varied and the accuracy is plotted against those values. To measure the
  accuracy, the true nearest neighbors are required, therefore
  :class:`sklearn.neighbors.NearestNeighbors` is used to compute the exact
  neighbors.
  """
  from __future__ import division
  print(__doc__)
  
  # Author: Maheshakya Wijewardena <maheshakya.10@cse.mrt.ac.lk>
  #
  # License: BSD 3 clause
  
  
  ###############################################################################
  import numpy as np
  from sklearn.datasets.samples_generator import make_blobs
  from sklearn.neighbors import LSHForest
  from sklearn.neighbors import NearestNeighbors
  import matplotlib.pyplot as plt
  
  
  # Initialize size of the database, iterations and required neighbors.
  n_samples = 10000
  n_features = 100
  n_queries = 30
  rng = np.random.RandomState(42)
  
  # Generate sample data
  X, _ = make_blobs(n_samples=n_samples + n_queries,
                    n_features=n_features, centers=10,
                    random_state=0)
  X_index = X[:n_samples]
  X_query = X[n_samples:]
  # Get exact neighbors
  nbrs = NearestNeighbors(n_neighbors=1, algorithm='brute',
                          metric='cosine').fit(X_index)
  neighbors_exact = nbrs.kneighbors(X_query, return_distance=False)
  
  # Set `n_candidate` values
  n_candidates_values = np.linspace(10, 500, 5).astype(np.int)
  n_estimators_for_candidate_value = [1, 5, 10]
  n_iter = 10
  stds_accuracies = np.zeros((len(n_estimators_for_candidate_value),
                              n_candidates_values.shape[0]),
                             dtype=float)
  accuracies_c = np.zeros((len(n_estimators_for_candidate_value),
                           n_candidates_values.shape[0]), dtype=float)
  
  # LSH Forest is a stochastic index: perform several iteration to estimate
  # expected accuracy and standard deviation displayed as error bars in
  # the plots
  for j, value in enumerate(n_estimators_for_candidate_value):
      for i, n_candidates in enumerate(n_candidates_values):
          accuracy_c = []
          for seed in range(n_iter):
              lshf = LSHForest(n_estimators=value,
                               n_candidates=n_candidates, n_neighbors=1,
                               random_state=seed)
              # Build the LSH Forest index
              lshf.fit(X_index)
              # Get neighbors
              neighbors_approx = lshf.kneighbors(X_query,
                                                 return_distance=False)
              accuracy_c.append(np.sum(np.equal(neighbors_approx,
                                                neighbors_exact)) /
                                n_queries)
  
          stds_accuracies[j, i] = np.std(accuracy_c)
          accuracies_c[j, i] = np.mean(accuracy_c)
  
  # Set `n_estimators` values
  n_estimators_values = [1, 5, 10, 20, 30, 40, 50]
  accuracies_trees = np.zeros(len(n_estimators_values), dtype=float)
  
  # Calculate average accuracy for each value of `n_estimators`
  for i, n_estimators in enumerate(n_estimators_values):
      lshf = LSHForest(n_estimators=n_estimators, n_neighbors=1)
      # Build the LSH Forest index
      lshf.fit(X_index)
      # Get neighbors
      neighbors_approx = lshf.kneighbors(X_query, return_distance=False)
      accuracies_trees[i] = np.sum(np.equal(neighbors_approx,
                                            neighbors_exact))/n_queries
  
  ###############################################################################
  # Plot the accuracy variation with `n_candidates`
  plt.figure()
  colors = ['c', 'm', 'y']
  for i, n_estimators in enumerate(n_estimators_for_candidate_value):
      label = 'n_estimators = %d ' % n_estimators
      plt.plot(n_candidates_values, accuracies_c[i, :],
               'o-', c=colors[i], label=label)
      plt.errorbar(n_candidates_values, accuracies_c[i, :],
                   stds_accuracies[i, :], c=colors[i])
  
  plt.legend(loc='upper left', fontsize='small')
  plt.ylim([0, 1.2])
  plt.xlim(min(n_candidates_values), max(n_candidates_values))
  plt.ylabel("Accuracy")
  plt.xlabel("n_candidates")
  plt.grid(which='both')
  plt.title("Accuracy variation with n_candidates")
  
  # Plot the accuracy variation with `n_estimators`
  plt.figure()
  plt.scatter(n_estimators_values, accuracies_trees, c='k')
  plt.plot(n_estimators_values, accuracies_trees, c='g')
  plt.ylim([0, 1.2])
  plt.xlim(min(n_estimators_values), max(n_estimators_values))
  plt.ylabel("Accuracy")
  plt.xlabel("n_estimators")
  plt.grid(which='both')
  plt.title("Accuracy variation with n_estimators")
  
  plt.show()
  