code: def adjusted_mutual_info_score(labels_true, labels_pred):
      """Adjusted Mutual Information between two clusterings.
  
      Adjusted Mutual Information (AMI) is an adjustment of the Mutual
      Information (MI) score to account for chance. It accounts for the fact that
      the MI is generally higher for two clusterings with a larger number of
      clusters, regardless of whether there is actually more information shared.
      For two clusterings :math:`U` and :math:`V`, the AMI is given as::
  
          AMI(U, V) = [MI(U, V) - E(MI(U, V))] / [max(H(U), H(V)) - E(MI(U, V))]
  
      This metric is independent of the absolute values of the labels:
      a permutation of the class or cluster label values won't change the
      score value in any way.
  
      This metric is furthermore symmetric: switching ``label_true`` with
      ``label_pred`` will return the same score value. This can be useful to
      measure the agreement of two independent label assignments strategies
      on the same dataset when the real ground truth is not known.
  
      Be mindful that this function is an order of magnitude slower than other
      metrics, such as the Adjusted Rand Index.
  
      Read more in the :ref:`User Guide <mutual_info_score>`.
  
      Parameters
      ----------
      labels_true : int array, shape = [n_samples]
          A clustering of the data into disjoint subsets.
  
      labels_pred : array, shape = [n_samples]
          A clustering of the data into disjoint subsets.
  
      Returns
      -------
      ami: float(upperlimited by 1.0)
         The AMI returns a value of 1 when the two partitions are identical
         (ie perfectly matched). Random partitions (independent labellings) have
         an expected AMI around 0 on average hence can be negative.
  
      See also
      --------
      adjusted_rand_score: Adjusted Rand Index
      mutual_information_score: Mutual Information (not adjusted for chance)
  
      Examples
      --------
  
      Perfect labelings are both homogeneous and complete, hence have
      score 1.0::
  
        >>> from sklearn.metrics.cluster import adjusted_mutual_info_score
        >>> adjusted_mutual_info_score([0, 0, 1, 1], [0, 0, 1, 1])
        1.0
        >>> adjusted_mutual_info_score([0, 0, 1, 1], [1, 1, 0, 0])
        1.0
  
      If classes members are completely split across different clusters,
      the assignment is totally in-complete, hence the AMI is null::
  
        >>> adjusted_mutual_info_score([0, 0, 0, 0], [0, 1, 2, 3])
        0.0
  
      References
      ----------
      .. [1] `Vinh, Epps, and Bailey, (2010). Information Theoretic Measures for
         Clusterings Comparison: Variants, Properties, Normalization and
         Correction for Chance, JMLR
         <http://jmlr.csail.mit.edu/papers/volume11/vinh10a/vinh10a.pdf>`_
  
      .. [2] `Wikipedia entry for the Adjusted Mutual Information
         <https://en.wikipedia.org/wiki/Adjusted_Mutual_Information>`_
  
      """
      labels_true, labels_pred = check_clusterings(
          labels_true, labels_pred
      )
      n_samples = labels_true.shape[0]
      classes = np.unique(labels_true)
      clusters = np.unique(labels_pred)
      # Special limit cases: no clustering since the data is not split.
      # This is a perfect match hence return 1.0.
      if (
          classes.shape[0] == clusters.shape[0] == 1
          or classes.shape[0] == clusters.shape[0] == 0
      ):
          return 1.0
      contingency = contingency_matrix(
          labels_true, labels_pred, sparse=True
      )
      contingency = contingency.astype(np.float64)
      # Calculate the MI for the two clusterings
      mi = mutual_info_score(
          labels_true, labels_pred, contingency=contingency
      )
      # Calculate the expected value for the mutual information
      emi = expected_mutual_information(contingency, n_samples)
      # Calculate entropy for each labeling
      h_true, h_pred = entropy(labels_true), entropy(labels_pred)
      ami = (mi - emi) / (max(h_true, h_pred) - emi)
      return ami
  
imports: from __future__ import division
  from math import log
  import numpy
  from scipy.misc import comb
  from scipy import sparse
  from .expected_mutual_info_fast import expected_mutual_information
  from ...utils.fixes import bincount
  from ...utils.validation import check_array
label_desc: Use image node_id 10 for calling a global function with example usage: adjusted_mutual_info_score(labels_true, labels_pred) and returns: ami, int