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Matrix Correlation

Published online by Cambridge University Press:  01 January 2025

J. O. Ramsay ,
Jos ten Berge  and
G. P. H. Styan
J. O. Ramsay*
Affiliation:
McGill University
Jos ten Berge
Affiliation:
University of Groningen
G. P. H. Styan
Affiliation:
McGill University
*
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Abstract

A correlational measure for an n by p matrix X and an n by q matrix Y 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 transformations XL and YM is discussed where one or both transformations are constrained to be orthogonal. Special attention is focussed on transformations which cause XL and YM to be n by s, where s may be any number between 1 and min (p, q). An efficient algorithm is described for maximizing the correlation between XL and YM 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.

Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 3 , September 1984 , pp. 403 - 423
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

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.

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