A Binary Integer Program to Maximize the Agreement Between Partitions

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 agre...

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Vydáno v:Journal of classification Ročník 25; číslo 2; s. 185 - 193
Hlavní autoři: Brusco, Michael J., Steinley, Douglas
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer-Verlag 01.11.2008
Springer
Springer Nature B.V
Témata:
Agreements
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
Heuristic
Integer programming
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
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Popis
Shrnutí: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.
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ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-008-9013-9