On the use of correlations to interpret canonical functions

Abstract

Two major types of canonical functions are considered, canonical discriminant functions that separate groups of observation vectors, and canonical variates associated with canonical correlations. The coefficients in both types of canonical functions reflect the joint contribution of the variables to the canonical functions. If the coefficients are converted to correlations, however, they merely reproduce univariate statistic values and become useless in gauging the importance of each variable in the context of the others.