Direct multicriteria clustering algorithms

In a multicriteria clustering problem, optimization over more than one criterion is required. The problem can be treated in different ways: by reduction to a clustering problem with the single criterion obtained as a combination of the given criteria; by constrained clustering algorithms where a selected critetion is considered as the clustering criterion and all others determine the constraints; or by direct algorithms. In this paper two types of direct algorithms for solving multicriteria clustering problem are proposed: the modified relocation algorithm, and the modified agglomerative algorithm. Different elaborations of these two types of algorithms are discussed and compared. Finally, two applications of the proposed algorithms are presented. Elaborated version of the talks presented at the First Conference of the International Federation of Classification Societies, Aachen, 1987, at the International Conference on Social Science Methodology, Dubrovnik, 1988, and at the Second Conference of the International Federation of Classification Societies, Charlottesville, 1989. This work was supported in part by the Research Council of Slovenia.