SOME METHODS OF CONSTRAINED CLUSTERING FOR QUALITATIVE DATA

This paper is concerned with a problem of constrained clustering for qualitative data. Combinatorial problem of scheduling meetings is a typical example. The desired schedule of meetings is such one that minimizes the total number of man-days. In those clustering problems, the computational time to find the optimal solution increases exponentially as the number of meetings grows. In order to find a near optimal solution efficiently, we discuss some methods; 1)methods based on quantification methods(Quantification Theory3, Karhunen-Loeve Expansion)and2)a Bottom-up Merging(Hierarchical Clustering)method which is derived from the inherent criterion of the problem. In method 2), particularly, the representative vector of each cluster and the metric for merging clusters are logically and uniquely determined by the criterion. It is shown by experiments that schedules obtained by these methods are better than those obtained in trial and error.