Nonlinear canonical correlation analysis with k sets of variables

The multivariate technique OVERALS is introduced as a non-linear generalization of canonical correlation analysis (CCA). First, two sets CCA is introduced. Two sets CCA is a technique that computes linear combinations of sets of variables that correlate in an optimal way. Two sets CCA is then expanded to generalized (or k sets) CCA. The formulation for the OVERALS technique fits well in the general tradition of "k" sets methods. The formulation is based on a minimization of the loss between object scores and canonical variates of all sets together, but is expanded with optimal scaling and the method of copies. Single and multiple transformations are discussed. The method is illustrated using data from an American consumer report giving the characteristics of 33 popular cars and 3 sets of data. Three tables and seven graphs present the data from the application study