Merging groups to maximize object partition comparison

Abstract

The problem of objectively comparing two independently determined partitions ofN objects or variables is discussed. A similarity measure based on the simple matching coefficient is defined and related to previously suggested measures. The problem of merging groups in one partition to maximize this similarity measure is discussed and formulated as a mathematical programming problem; such an approach is useful for determining to what extent the groups in one partition merely represent a finer subdivision of the groups in the other partition. By exploiting the structure of the similarity measure, an efficient algorithm is developed to determine which groups (if any) should be merged to maximize partition similarity.