Consensus indices for comparing classifications

Abstract

Methods for measuring the degree of agreement between dendrograms (which correspond uniquely to hierarchic nested classifications) are discussed. While some methods take the relative levels of the subsets into account, most presently available methods do not. A previously proposed consensus index is shown to have a maximum possible value that is (for a given number of objects) a function of the balance (the degree to which the subsets of each set are equal in size) of the consensus of the two classifications being compared. A new consensus index is proposed that does not have this defect. In addition, a new index is proposed that is the proportion of all possible classifications that contain the sets that are in the consensus of the two dendrograms being compared. A table giving the numbers of possible bifurcating dendrograms (up to t=100 objects) is furnished to assist in the computation of this latter index. © 1982.