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.
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Albers CJ (2008) Some quadratic optimisation problems in psychometrics. In: Shigemasu K (ed) New trends in psychometrics. Universal Academic Press, Tokyo, pp 1–6
Albers CJ, Critchley F, Gower JC (2010) Quadratic minimisation problems in statistics. J Multivariate Anal. doi:10.1016/j.jmva.2009.12.018
Albers CJ, Critchley F, Gower JC (2010) Explicit minimisation of a convex quadratic under a quadratic constraint (In preparation)
Commandeur JJF (1991) Matching configurations. DSWO Press, Leiden
Gower JC, Dijksterhuis GB (2004) Procrustes problems. Oxford Statistical Science Series 30. University Press, Oxford
ten Berge JMF, Kiers HAL, Commandeur JJF (1993) Orthogonal Procrustes rotation for matrices with missing values. Br J Math Stat Psychol 46(1): 119–134
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Open Access This 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.
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Albers, C.J., Gower, J.C. A general approach to handling missing values in Procrustes analysis. Adv Data Anal Classif 4, 223–237 (2010). https://doi.org/10.1007/s11634-010-0077-0
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DOI: https://doi.org/10.1007/s11634-010-0077-0