An integrated approach is proposed to solve the Constrained Clustering problems which are oriented on taking the opinion of a group of experts into account. A cluster and the objects to be clustered are proposed to be represented as multisets, and the distance between these to be determined by metrics in the Petrovsky multisets space. The approach is implemented within the Constraint Programming paradigm. In so doing, the significant complexity is in organizing effective processing the qualitative constraints, namely, the rules for assigning the objects to one or different clusters. The qualitative constraints are proposed to be represented and processed as table constraints of a new type, i.e., as the smart-tables of D-type. The main attention is confined to the problem of how to reduce the amount of constraints and how to simplify the Constrained Clustering problem. It is proposed to generate constraints for some pairs of objects rather than for all of them, with the generation based on a priori interval estimation of the optimal value of the clustering criterion. To do that, a modified method of multisets hierarchical clustering has been proposed. The approach proposed allows a global optimum to be found for the Constrained Clustering problems considered.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.