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: Regressor
Output Range: -1 to 1
Parameters#
This metric does not have any parameters.
Example#
use Rubix\ML\CrossValidation\Metrics\RandIndex;
$metric = new RandIndex();
References#
-
W. M. Rand. (1971). Objective Criteria for the Evaluation of Clustering Methods. ↩
Last update:
2021-03-03