, Volume 57, Issue 3, pp 371–382 | Cite as

Minimization of a class of matrix trace functions by means of refined majorization

  • Henk A. L. Kiers
  • Jos M. F. ten Berge


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.

Key words

trace optimization majorization alternating least squares 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bijleveld, C. J. H. (1989).Exploratory linear dynamical systems analysis. Leiden: DSWO Press.Google Scholar
  2. 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
  3. Bijleveld, C., & de Leeuw, J. (1991). Fitting longitudinal reduced rank regression models by alternating least squares.Psychometrika, 56, 433–447.CrossRefGoogle Scholar
  4. Cliff, N. (1966). Orthogonal rotation to congruence.Psychometrika, 31, 33–42.CrossRefGoogle Scholar
  5. 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.Google Scholar
  6. Kiers, H. A. L. (1990). Majorization as a tool for optimizing a class of matrix functions.Psychometrika, 55, 417–428.Google Scholar
  7. Koschat, M. A., & Swayne, D. F. (1991). A weighted Procrustes Criterion.Psychometrika, 56, 229–239.CrossRefGoogle Scholar
  8. Mooijaart A., & Commandeur, J. J. F. (1990). A general solution of the weighted orthonormal Procrustes problem.Psychometrika, 55, 657–663.CrossRefGoogle Scholar
  9. Rao, C. R. (1980). Matrix approximations and reduction of dimensionality in multivariate statistical analysis. In P. R. Krishnaiah (Ed.),Multivariate analysis V (pp. 3–22). Amsterdam: North-Holland.Google Scholar
  10. Roth, W. E. (1934). On direct product matrices.Bulletin of the American Mathematical Society, 40, 461–468.Google Scholar
  11. Takane, Y., & Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables.Psychometrika, 56, 97–120.Google Scholar

Copyright information

© The Psychometric Society 1992

Authors and Affiliations

  • Henk A. L. Kiers
    • 1
  • Jos M. F. ten Berge
    • 1
  1. 1.University of GroningenThe Netherlands

Personalised recommendations