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Anisotropic generalized Procrustes analysis

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  • Bennani Dosse, Mohammed
  • Kiers, Henk A.L.
  • Ten Berge, Jos M.F.

Abstract

Generalized Procrustes analysis is a popular method for matching several configurations by translations, rotations/reflections and scaling constants. It aims at producing a group average from these Euclidean similarity transformations followed by bi-linear approximation of this group average for graphical inspection. An extension that allows for anisotropic scaling (i.e. different scaling of different dimensions) is proposed. This method is illustrated using two real data sets from sensory analysis.

Suggested Citation

  • Bennani Dosse, Mohammed & Kiers, Henk A.L. & Ten Berge, Jos M.F., 2011. "Anisotropic generalized Procrustes analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1961-1968, May.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:5:p:1961-1968
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    References listed on IDEAS

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    1. Edmund Peay, 1988. "Multidimensional rotation and scaling of configurations to optimal agreement," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 199-208, June.
    2. Bert Green, 1952. "The orthogonal approximation of an oblique structure in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 429-440, December.
    3. Jos Berge & Dirk Knol, 1984. "Orthogonal rotations to maximal agreement for two or more matrices of different column orders," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 49-55, March.
    4. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
    5. Byron J. T. Morgan, 1989. "Introduction to Optimization," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 152(2), pages 254-255, March.
    6. J. Gower, 1975. "Generalized procrustes analysis," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 33-51, March.
    7. Mohammed Bennani Dosse & Jos Berge, 2010. "Anisotropic Orthogonal Procrustes Analysis," Journal of Classification, Springer;The Classification Society, vol. 27(1), pages 111-128, March.
    8. Jos Berge, 1977. "Orthogonal procrustes rotation for two or more matrices," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 267-276, June.
    9. James Lingoes & Ingwer Borg, 1978. "A direct approach to individual differences scaling using increasingly complex transformations," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 491-519, December.
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