A cophenetic correlation coefficient for the modified Tocher's method

Abstract

The cophenetic correlation coefficient has usually been taken as a measure of clustering consistence. However, its use has been restricted for hierarchical methods, at which is possible to obtain a cophenetic matrix. Nevertheless, Silva and Dias (2013) have proposed a simple algorithm to compute the cophenetic matrix for the original Tocher's method. Following the premise at which cophenetic values can be obtained even by ordination methods, the goal of this work is to extend that algorithm for computing the cophenetic matrix in cluster analysis performed via  modified Tocher's method and then to estimate the cophenetic correlation. To illustrate the procedure, we used two measure of distance: the squared generalized Mahalanobis and the Euclidean distance, based on six morphological characters of garlic cultivars. We performed comparisons of outcomes obtained with two hierarchical methods: Ward's algorithm and the average linkage. As expected, most of our results are according with those found by Silva and Dias (2013). The clustering consistence of agglomerative methods and the original and modified Tocher's can be evaluated by using a criterion in common, the correlation between original and cophenetic distances.