Comparing Two Partitions Obtained on Different Sets of Units

Rand Index (Rand 1971) is known as one of the most common indices for comparing two partitions obtained on the same sets of units. It can take the value on the interval between 0 and 1 where higher value indicates more similar partitions. When measuring the similarity of two partitions the splitting and merging of clusters can be considered as factors with different effects on the value of an index. The Rand Index belongs to a group of symmetric indices in this context since both merging and splitting have a negative effect on the value of the measure. When the splitting and merging of groups have to be considered differently - according to the operationalization of studied groups - one of the Wallace indices can be used (Wallace 1983). Here, only the merging or only the splitting of groups lowers the value of an index.

In the case when two partitions are obtained on two different sets of units with a non-empty intersection, the number of in-coming and out-going units (e.g., when the sets of units are obtained in different time points) can be considered as a factors which lowers the value of an index. Therefore the two symmetric modified Rand indices and two asymmetric Wallace indices will be presented along with the correction for chance, which enables to compare the values of indices obtained on different partitions.