Editing Cluster analysis (section)

==== [[Rand index]] ====
The Rand index<ref>{{Cite journal
 | first = W. M. | last = Rand
 | title = Objective criteria for the evaluation of clustering methods
 | journal = [[Journal of the American Statistical Association]]
 | volume = 66
 | pages = 846–850
 | year = 1971
 | doi = 10.2307/2284239
 | issue = 336
 | publisher = American Statistical Association
 | jstor = 2284239
| arxiv = 1704.01036
 }}</ref> computes how similar the clusters (returned by the clustering algorithm) are to the benchmark classifications. It can be computed using the following formula:
:<math>
RI = \frac {TP + TN} {TP + FP + FN + TN}
</math>
where  <math>TP</math> is the number of true positives, <math>TN</math> is the number of [[true negative]]s, <math>FP</math> is the number of [[false positives]], and <math>FN</math> is the number of [[false negatives]]. The instances being counted here are the number of correct ''pairwise'' assignments. That is, <math>TP</math> is the number of pairs of points that are clustered together in the predicted partition and in the ground truth partition, <math>FP</math> is the number of pairs of points that are clustered together in the predicted partition but not in the ground truth partition etc. If the dataset is of size N, then <math>TP + TN + FP + FN = \binom{N}{2}</math>. 
One issue with the [[Rand index]] is that [[false positive]]s and [[false negative]]s are equally weighted. This may be an undesirable characteristic for some clustering applications. The F-measure addresses this concern,{{Citation needed|date=May 2018|reason=it does not achieve the same for chance correction as ARI}} as does the chance-corrected [[adjusted Rand index]].