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Rand Index#

The Adjusted Rand Index is a measure of similarity between a clustering and some ground-truth that is adjusted for chance. It considers all pairs of samples that are assigned in the same or different clusters in the predicted and empirical clusterings.

\[ {\displaystyle ARI = {\frac {\left.\sum _{ij}{\binom {n_{ij}}{2}}-\left[\sum _{i}{\binom {a_{i}}{2}}\sum _{j}{\binom {b_{j}}{2}}\right]\right/{\binom {n}{2}}}{\left.{\frac {1}{2}}\left[\sum _{i}{\binom {a_{i}}{2}}+\sum _{j}{\binom {b_{j}}{2}}\right]-\left[\sum _{i}{\binom {a_{i}}{2}}\sum _{j}{\binom {b_{j}}{2}}\right]\right/{\binom {n}{2}}}}} \]

Estimator Compatibility: Clusterer

Score Range: -1 to 1


This metric does not have any parameters.


use Rubix\ML\CrossValidation\Metrics\RandIndex;

$metric = new RandIndex();


  1. W. M. Rand. (1971). Objective Criteria for the Evaluation of Clustering Methods.