Explicit agreement extremes for a $2\times2$ table with given marginals
This work addresses a theoretical problem in clustering analysis, but it is incremental as it extends existing numerical methods to an explicit solution for a limited scenario.
The paper tackled the problem of finding explicit solutions for maximizing or minimizing agreement between two clusterings with two clusters each, given fixed marginals, which previously required numerical algorithms. It provided an explicit solution for this specific case.
The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures. Until now, it was possible to find its solution only through numerical algorithms. Here, an explicit solution is shown for the case where the two clusterings have two clusters each.