A cophenetic correlation coefficient for Tocher’s method

Abstract

The objective of this work was to propose a way of using the Tocher’s method of clustering to obtain a matrix similar to the cophenetic one obtained for hierarchical methods, which would allow the calculation of a cophenetic correlation. To illustrate the obtention of the proposed cophenetic matrix, we used two dissimilarity matrices – one obtained with the generalized quadratic Mahalanobis distance and the other with the Euclidean distance – between 17 garlic cultivars, based on six morphological characters. Basically, the proposal for obtaining the cophenetic matrix was to use the average distances within and between clusters, after performing the clustering. A function in R language was proposed to compute the cophenetic matrix for Tocher’s method. The empirical distribution of this correlation coefficient was briefly studied. For both dissimilarity measures, the values of cophenetic correlation obtained for the Tocher’s method were higher than those obtained with the hierarchical methods (Ward’s algorithm and average linkage – UPGMA). Comparisons between the clustering made with the agglomerative hierarchical methods and with the Tocher’s method can be performed using a criterion in common: the correlation between matrices of original and cophenetic distances.