Computes the Adjusted Mutual Information (AMI) from a contingency table.
The AMI measures the mutual information between two clusterings, adjusted
for chance. Values range from 0 to 1, where 1 indicates perfect agreement
and 0 indicates independence.
Usage
ami_from_contingency(cont_table)
Arguments
- cont_table
A contingency table (matrix) where rows correspond to
clusters in the first assignment and columns to clusters in the second.
Value
A numeric value representing the Adjusted Mutual Information.
Details
The Adjusted Mutual Information is calculated as:
$$AMI = \frac{MI - E[MI]}{\max(H(U), H(V)) - E[MI]}$$
where \(MI\) is the mutual information, \(E[MI]\) is the expected mutual
information under random permutation, and \(H(U)\) and \(H(V)\) are the
entropies of the two clusterings.
References
Vinh, N. X., Epps, J., and Bailey, J. (2010). Information theoretic measures
for clusterings comparison: Variants, properties, normalization and correction
for chance. Journal of Machine Learning Research, 11, 2837-2854.