Procrustes methods

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



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,....,XK ΤK in which case their average (the group average) is important. Applications are in shape analysis, image analysis, psychometrics etc.

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