Clustering by Identification with Special Application to Two-Way Tables of Counts

The formation of a partition of objects, each with an associated random measurement X, is given operational meaning and a figure of merit. The information about X, given each object, is first reduced to information about X, given the cluster in the partition to which that object belongs. The figure of merit for a partition is then the probability of a correct object identification, on the basis of a realization of X, after the information loss. An algorithm is derived for performing the calculations on two-way tables of counts.