The comparison and fitting of given classification schemes

A permutation procedure is described for statistically comparing a given classification scheme, characterized as a hierarchically organized collection of subsets, to either a proximity matrix or a second classification scheme defined on the same basic set of objects. To prevent a bias that may result when an optimization method is used to construct the classification structures being considered, it is assumed that the desired comparisons involve classifications and/or proximities that have been derived from separate sources. In addition to an extensive number of examples used to clarify the major points in the presentation of the inference strategy, several heuristic optimization techniques are also introduced and illustrated. These latter procedures attempt to “fit” the form of a target classification structure by relabeling the rows and simultaneously the columns of a given proximity matrix to maximize the correspondence between the fixed target and the relabeled proximity matrix.