adjusted_mutual_information(first_partition: object, second_partition: object) → cdlib.evaluation.comparison.MatchingResult

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 \(U\) and \(V\), 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.

  • first_partition – NodeClustering object
  • second_partition – NodeClustering object

MatchingResult object

>>> from cdlib import evaluation, algorithms
>>> g = nx.karate_club_graph()
>>> louvain_communities = algorithms.louvain(g)
>>> leiden_communities = algorithms.leiden(g)
>>> evaluation.adjusted_mutual_information(louvain_communities,leiden_communities)
  1. Vinh, N. X., Epps, J., & Bailey, J. (2010). Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research, 11(Oct), 2837-2854.