Clusterwise aggregation of relations

In this paper we handle the general problem of finding q(> 1) central relations on a set of objects which best fit the information contained in a finite number of given relations on that set. The proposed CAR (clusterwise aggregation of relations) algorithm allows one to consider the well-known situation of determining a single central relation as a special case (q = 1) and takes into account the fact that the representation of appropriately selected subsets of relations by different central relations can provide additional insights into whether different clusters or segments of relations exist in the given set of relations. Two examples demonstrate the usefulness of the suggested approach.