Matrix correlation

A correlational measure for ann byp matrixX and ann byq matrixY assesses their relation without specifying either as a fixed target. This paper discusses a number of useful measures of correlation, with emphasis on measures which are invariant with respect to rotations or changes in singular values of either matrix. The maximization of matrix correlation with respect to transformationsXL andYM is discussed where one or both transformations are constrained to be orthogonal. Special attention is focussed on transformations which causeXL andYM to ben bys, wheres may be any number between 1 and min (p, q). An efficient algorithm is described for maximizing the correlation betweenXL andYM where analytic solutions do not exist. A factor analytic example is presented illustrating the advantages of various coefficients and of varying the number of columns of the transformed matrices.This research was supported by grant APA 0320 from the Natural Sciences and Engineering Research Council of Canada. The authors wish to acknowledge valuable discussion of this problem with Jan de Leeuw, University of Leiden.