Randindex

Randindex, or Rand index, is a measure of the similarity between two data clusterings of the same dataset. It assesses how well two partitions agree on the grouping of items, by considering all pairs of items and counting those that are either clustered together in both partitions or clustered apart in both partitions. The index ranges from 0 to 1, with 1 indicating perfect agreement.

To compute the Rand index, consider all unordered pairs of items. Classify each pair into four categories: a = pairs placed in the same cluster in both partitions; b = pairs placed in different clusters in both partitions; c = pairs placed in the same cluster in the first partition but in different clusters in the second; d = pairs placed in different clusters in the first partition but in the same cluster in the second. Let N be the total number of pairs, N = C(n, 2). The Rand index is R = (a + b) / (a + b + c + d) = (a + b) / N. A related computation can be performed using the contingency table of the two clusterings, but the pair-counting formulation is most straightforward.

Limitations include its sensitivity to chance: even random labelings can yield nonzero values, especially with many clusters. Therefore, the Adjusted Rand Index (ARI) is often preferred, as it corrects for chance and yields a value of 1 for perfect agreement, near 0 for random labeling, and can be negative in some cases.

The Rand index was introduced by William M. Rand in 1971 and remains a foundational tool for evaluating clustering results. It is widely used in machine learning, bioinformatics, image analysis, and related fields to compare clustering outputs to ground truth or to another clustering.