Rand Index. Rand index is defined as the number of pairs of objects
that are either in the same group or in different groups in both partitions
divided by the total number of pairs of objects. The Rand index lies between
0 and 1. When two partitions agree perfectly, the Rand index achieves the
maximum value 1. A problem with Rand index is that the expected value of
the Rand index between two random partitions is not a constant. This problem
is corrected by the adjusted Rand index that assumes the generalized
hyper-geometric distribution as the model of randomness. The adjusted Rand
index has the maximum value 1, and its expected value is 0 in the case
of random clusters. A larger adjusted Rand index means a higher agreement
between two partitions. The adjusted Rand index is recommended for measuring
agreement even when the partitions compared have different numbers of clusters.