A Note on Maximizing the Agreement Between Partitions: A Stepwise Optimal Algorithm and Some Properties

Building on Brusco and Steinley (2008), a computationally efficient stepwise optimal heuristic is provided for maximizing the adjusted Rand index (Hubert and Arabie 1985). The proposed algorithm is different than other methods for estimating the maximum value for the adjusted Rand index (e.g., Messatfa 1992) in that it does not rely on mathematical programming; consequently, problems of much larger size can be handled. Using the proposed method, various characteristics of the adjusted Rand index are explored and presented.