Analysis of K sets of data, with differential emphasis on agreement between and within sets

A general class of methods for (partial) rotation of a set of (loading) matrices to maximal agreement has been available in the literature since the 1980s. It contains a generalization of canonical correlation analysis as a special case. However, various other generalizations of canonical correlation analysis have been proposed. A new general class of methods for each such alternative generalization of canonical correlation is proposed. Together, these general classes of methods form a superclass of methods that strike a compromise between explaining the variance within sets of variables and explaining the agreement between sets of variables, as illustrated in some examples. Furthermore, one general algorithm for finding the solutions for all methods in all general classes is offered. As a consequence, for all methods in the superclass of methods, algorithms are available at once. For the existing methods, the general algorithm usually reduces to the standard algorithms employed in these methods, and thus the algorithms for all these methods are shown to be related to each other.