Procrustes methods

The basic Procrustes problem is to transform a matrix X-1 to X1T in order to match a target matrix X-2. Matching necessitates that X-1 and X-2 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 X1T1,..., XKTK, in which case their average (the group average) is important. Applications are in shape analysis, image analysis, psychometrics etc. (C) 2010 John Wiley & Sons, Inc.