A Binary Integer Program to Maximize the Agreement Between Partitions

• Published in: Journal of classification Vol. 25; no. 2; pp. 185 - 193
• Main Authors: Brusco, Michael J., Steinley, Douglas
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.11.2008; Springer; Springer Nature B.V
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Binary system; Bioinformatics; Calculus of variations and optimal control; Classification; Computer science; control theory; systems; Exact sciences and technology; Marketing; Mathematical analysis; Mathematics; Mathematics and Statistics; Methods of scientific computing (including symbolic computation, algebraic computation); Multivariate analysis; Numerical analysis. Scientific computation; Pattern Recognition; Probability and statistics; Psychometrics; Sciences and techniques of general use; Signal,Image and Speech Processing; Statistical Theory and Methods; Statistics; Studies; Theoretical computing; Partition agreement; Contingency table; Binary integer programming; Partition; Discriminant analysis; Data analysis; Multivariate analysis; Exact solution; Integer; Integer programming; Transportation problem; Optimal solution; Marginal distribution
• ISSN: 0176-4268; 1432-1343
• DOI: 10.1007/s00357-008-9013-9

This research note focuses on a problem where the cluster sizes for two partitions of the same object set are assumed known; however, the actual assignments of objects to clusters are unknown for one or both partitions. The objective is to find a contingency table that produces maximum possible agreement between the two partitions, subject to constraints that the row and column marginal frequencies for the table correspond exactly to the cluster sizes for the partitions. This problem was described by H. Messatfa ( Journal of Classification , 1992, pp. 5–15), who provided a heuristic procedure based on the linear transportation problem. We present an exact solution procedure using binary integer programming. We demonstrate that our proposed method efficiently obtains optimal solutions for problems of practical size.