Procrustes methods

Gower, John C. (2010). Procrustes methods. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4) pp. 503–508.

DOI: https://doi.org/10.1002/wics.107

Abstract

The basic Procrustes problem is to transform a matrix X₁ to X₁Τ in order to match a target matrix X₂. Matching necessitates that X₁ and X₂ have the same number of rows identified with the same entities but the columns are unrestricted in type and number. Special cases discussed are when T is an orthogonal, projection, or direction-cosine matrix. Sometimes, both matrices are transformed and size parameters referring to isotropic and various forms of anisotropic scaling may be incorporated. Procrustes methods may be generalized to cover K transformed matrices X₁ Τ₁,....,X_K Τ_K in which case their average (the group average) is important. Applications are in shape analysis, image analysis, psychometrics etc.

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