cdlib.evaluation.rmi

cdlib.evaluation.rmi(first_partition: object, second_partition: object, norm_type: str = 'none', logbase: int = 2) → MatchingResult

This function calculates the Reduced Mutual Information (RMI) between two clusterings.

\[RMI = MI(c1, c2) - \log \frac{Omega(a, b)}{n}\]

where MI(c1, c2) is mutual information of the clusterings c1 and c2, and Omega(a, b) is the number of contingency tables with row and column sums equal to a and b.

Parameters:

  • first_partition – NodeClustering object

  • second_partition – NodeClustering object

  • norm_type – The normalization types are: ‘none’ returns the RMI without a normalization; ‘normalized’ returns the RMI with upper bound equals to 1.

  • logbase – int, default 2

Returns:

MatchingResult object

Example:

>>> from cdlib import evaluation, algorithms
>>> import networkx as nx
>>> g = nx.karate_club_graph()
>>> louvain_communities = algorithms.louvain(g)
>>> leiden_communities = algorithms.leiden(g)
>>> evaluation.rmi(louvain_communities,leiden_communities)
Reference:

      1. Newman, George T. Cantwell, and Jean-Gabriel Young. Improved mutual information measure for classification and community detection. arXiv:1907.12581, 2019.

Note

The function requires the clusim library to be installed. You can install it via pip: pip install clusim