A monotonically convergent algorithm for orthogonal congruence rotation

Henk A.L. Kiers, Patrick J.F. Groenen

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)

Abstract

Brokken has proposed a method for orthogonal rotation of one matrix such that its columns have a maximal sum of congruences with the columns of a target matrix. This method employs an algorithm for which convergence from every starting point is not guaranteed. In the present paper, an iterative majorization algorithm is proposed which is guaranteed to converge from every starting point. Specifically, it is proven that the function value converges monotonically, and that the difference between subsequent iterates converges to zero. In addition to the better convergence properties, another advantage of the present algorithm over Brokken's one is that it is easier to program. The algorithms are compared on 80 simulated data sets, and it turned out that the new algorithm performed well in all cases, whereas Brokken's algorithm failed in almost half the cases. The derivation of the algorithm is given in full detail because it involves a series of inequalities that can be of use to derive similar algorithms in different contexts.

Original languageEnglish
Pages (from-to)375-389
Number of pages15
JournalPsychometrika
Volume61
Issue number2
DOIs
Publication statusPublished - Jun-1996

Keywords

  • optimization
  • majorization
  • matching
  • Procrustes rotation
  • PROCRUSTES

Cite this