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Advances in Data Analysis and Classification

, Volume 4, Issue 4, pp 223–237 | Cite as

A general approach to handling missing values in Procrustes analysis

  • Casper J. AlbersEmail author
  • John C. Gower
Open Access
Regular Article

Abstract

General Procrustes analysis is concerned with transforming a set of given configuration matrices to closest agreement. This paper introduces an approach useful for handling missing values in the configuration matrices in the context of general linear transformations. Centring and/or standardisation are allowed. Simplifications occur in the important case where the transformations are orthogonal. In the most general case, an interesting quadratic constrained optimisation problem appears.

Keywords

Procrustes analysis Missing value estimation Constrained optimisation 

Mathematics Subject Classification (2000)

65F30 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Albers CJ (2008) Some quadratic optimisation problems in psychometrics. In: Shigemasu K (ed) New trends in psychometrics. Universal Academic Press, Tokyo, pp 1–6Google Scholar
  2. Albers CJ, Critchley F, Gower JC (2010) Quadratic minimisation problems in statistics. J Multivariate Anal. doi: 10.1016/j.jmva.2009.12.018
  3. Albers CJ, Critchley F, Gower JC (2010) Explicit minimisation of a convex quadratic under a quadratic constraint (In preparation)Google Scholar
  4. Commandeur JJF (1991) Matching configurations. DSWO Press, LeidenGoogle Scholar
  5. Gower JC, Dijksterhuis GB (2004) Procrustes problems. Oxford Statistical Science Series 30. University Press, OxfordGoogle Scholar
  6. ten Berge JMF, Kiers HAL, Commandeur JJF (1993) Orthogonal Procrustes rotation for matrices with missing values. Br J Math Stat Psychol 46(1): 119–134zbMATHGoogle Scholar

Copyright information

© The Author(s) 2010

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Department of Psychometrics and Statistical MethodsUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK

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