Randindeks

Randindeks, or Rand index, is a measure of similarity between two data clusterings or partitions of the same dataset. It evaluates how much two partitions agree in terms of which pairs of elements should be grouped together or separated.

Computation is typically done from a contingency table. Let P and Q be two partitions of n elements, and let n_ij be the number of elements that are in cluster i in P and cluster j in Q. Define n_i. = sum_j n_ij (the size of P’s cluster i), n_.j = sum_i n_ij (the size of Q’s cluster j), and N = binomial(n, 2) (the total number of element pairs). Then

A = sum_i binomial(n_i., 2),

B = sum_j binomial(n_.j, 2),

C = sum_{i,j} binomial(n_ij, 2).

The Rand index is RI = 1 - (A + B - 2C) / N.

Equivalently, RI can be interpreted as the proportion of pairs for which the two partitions agree, i.e., either they are in the same cluster in both partitions or in different clusters in both partitions.

Interpretation and use are straightforward but with caveats. The Rand index ranges from 0 to 1, with 1 indicating identical partitions. It is not adjusted for chance, which can inflate scores when the number of clusters differs between partitions. For this reason, the Adjusted Rand Index (ARI) is often preferred when comparing clusterings across datasets or with different numbers of clusters.

See also: Adjusted Rand Index.