Minimum adjusted Rand index for two clusterings of a given size
This work addresses a theoretical problem in cluster analysis for researchers, but it is incremental as it builds on existing understanding of ARI extremes.
The paper derived an explicit formula for the minimum possible value of the adjusted Rand index (ARI) for two clusterings of given sizes, and provided a specific pair of clusterings that achieves this bound.
The adjusted Rand index (ARI) is commonly used in cluster analysis to measure the degree of agreement between two data partitions. Since its introduction, exploring the situations of extreme agreement and disagreement under different circumstances has been a subject of interest, in order to achieve a better understanding of this index. Here, an explicit formula for the lowest possible value of the ARI for two clusterings of given sizes is shown, and moreover a specific pair of clusterings achieving such a bound is provided.