Optimal clustering

Cluster analysis can be performed with several models. One method is to seek those clusters for which the total flow between all within-cluster members is a maximum. This model has, until now, been viewed as mathematically difficult because of the presence of products of integer variables in the objective function. In another optimization model of cluster analysis, the <i>p</i>-median, a central member is found for each cluster, so that relationships of cluster members with the various central members are maximized (or minimized). This problem, although mathematically tractable, is a less realistic formulation of the general clustering problem.The formulation of the maximum interflow problem is here transformed in stages into a linear analogue which is economically solvable. Computation experience with the several transformed stages is reported and a practical example of the analysis demonstrated.