Comparison of Ultrametrics Obtained With Real Data, Using the P L and VAL Aw Coefficients

Abstract

We compare 20 ultrametric matrices generated by the classifications obtained from 20 similarity indices for binary variables on the same group of data, that were studied by Hubálek (1982). To measure the similarity between the ultrametric matrices we use the P L coefficient proposed by Le Calvé (1977) and the Validity of Affinity Coefficient WW, VAL Aw proposed by Bacelar-Nicolau (1988). By means of hierarchical cluster analysis and principal component analysis on the similarity matrices obtained with those two coefficients, we draw conclusions about the 20 similarity indices and compare results for P L and VAL Aw coefficients. The results obtained with these two coefficients are very similar and are also similar to the results obtained by Hubálek. Finally we introduce in this ultrametrics/coefficients comparative study the simple matching coefficient, Sokal and Michener (1958), and observe, using P L or VAL Aw coefficients, its particular behaviour in relation to the other indices.