On comparing partitions

Rand (1971) proposed the Rand Index to measure the stability of two partitions of one set of units. Hubert and Arabie (1985) corrected the Rand Index for chance (Adjusted Rand Index). In this paper, we present some alternative indices. The proposed indices do not assume one set of units for two partitions. Here, one set of units can be a subset of the other set of units. According to the purpose of the comparison of two partitions, the merging and splitting of clusters in two partitions can have different impact on the value of the indices. Therefore, we proposed different modified Rand Indices.