Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-08T09:22:35.939Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimization of a Class of Matrix Trace Functions by means of Refined Majorization

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers  and
Jos M. F. ten Berge
Henk A. L. Kiers*
Affiliation:
University of Groningen
Jos M. F. ten Berge
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Henk A. L. Kiers, Department of Psychology, Grote Kruisstr. 2/1, 9712 TS Groningen, THE NETHERLANDS.
Get access Rights & Permissions [Opens in a new window]

Abstract

A procedure is described for minimizing a class of matrix trace functions. The procedure is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization. It contains a recently proposed algorithm by Koschat and Swayne for weighted Procrustes rotation as a special case. A number of trial analyses demonstrate that the refined majorization procedure is more efficient than the earlier majorization-based procedure.

Keywords

trace optimizationmajorizationalternating least squares
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 3 , September 1992 , pp. 371 - 382
Copyright
Copyright © 1992 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The research of H. A. L. Kiers has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences.

References

Bijleveld, C. J. H. (1989). Exploratory linear dynamical systems analysis, Leiden: DSWO Press.Google Scholar
Bijleveld, C., & de Leeuw, J. (1987, June). Fitting linear dynamical systems by alternating least squares. Paper presented at the European Meeting of the Psychometric Society, Twente, The Netherlands.Google Scholar
Bijleveld, C., de Leeuw, J. (1991). Fitting longitudinal reduced rank regression models by alternating least squares. Psychometrika, 56, 433–447.CrossRefGoogle Scholar
Cliff, N. (1966). Orthogonal rotation to congruence. Psychometrika, 31, 33–42.CrossRefGoogle Scholar
Henderson, H. V., Searle, S. R. (1981). The vec-permutation matrix, the vec operator and Kronecker products: A review. Linear and multilinear algebra, 9, 271–288.CrossRefGoogle Scholar
Kiers, H. A. L. (1990). Majorization as a tool for optimizing a class of matrix functions. Psychometrika, 55, 417–428.CrossRefGoogle Scholar
Koschat, M. A., Swayne, D. F. (1991). A weighted Procrustes Criterion. Psychometrika, 56, 229–239.CrossRefGoogle Scholar
Mooijaart, A., Commandeur, J. J. F. (1990). A general solution of the weighted orthonormal Procrustes problem. Psychometrika, 55, 657–663.CrossRefGoogle Scholar
Rao, C. R. (1980). Matrix approximations and reduction of dimensionality in multivariate statistical analysis. In Krishnaiah, P. R. (Eds.), Multivariate analysis V (pp. 3–22). Amsterdam: North-Holland.Google Scholar
Roth, W. E. (1934). On direct product matrices. Bulletin of the American Mathematical Society, 40, 461–468.CrossRefGoogle Scholar
Takane, Y., Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables. Psychometrika, 56, 97–120.CrossRefGoogle Scholar