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A cutting plane algorithm for a clustering problem. (English) Zbl 0675.90072

Summary: We consider a clustering problem that arises in qualitative data analysis. This problem can be transformed to a combinatorial optimization problem, the clique partitioning problem. We have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope. These theoretical results are utilized in this paper. We describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before. We discuss some details of the implementation of our code and present our computational results. We mention applications from, e.g., zoology, economics, and the political sciences.

MSC:

90C27 Combinatorial optimization
52Bxx Polytopes and polyhedra
62H30 Classification and discrimination; cluster analysis (statistical aspects)
90C90 Applications of mathematical programming

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