• $a$, the number of pairs of elements in $S$ that are in the same set in $X$ and in the same set in $Y$


• $b$, the number of pairs of elements in $S$ that are in different sets in $X$ and in different sets in $Y$


• $c$, the number of pairs of elements in $S$ that are in the same set in $X$ and in different sets in $Y$


• $d$, the number of pairs of elements in $S$ that are in different sets in $X$ and in the same set in $Y$

The Rand index, $R$, is:

• W. M. Rand, ''Objective criteria for the evaluation of clustering methods''. Journal of the American Statistical Association, 66, pp846–850 (1971).


• K. Y. Yeung, W. L. Ruzzo, ''Details of the Adjusted Rand index and Clustering algorithms'', Bioinformatics. {Link without Title}

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