Peter H. Schonemann and Robert M. Carroll
Fitting one matrix to another under choice of a central dilation and a rigid motion
Psychometrika, 1970, 35, 245-255
A least squares method is presented for fitting a given matrix A to another given matrix B under choice of an unknown rotation, an unknown translation and an unknown central dilation.
The procedure may be useful to investigators who wish to compare results obtained with non-metric scaling techniquesn across samples, or who wish to compare such results with those obtained by conventional factor analytic techniques on the same sample.
Technically a straightforward generalization of the orthogonal Procrustes problem, the utility of this particular least squares method extended beyond the narrow confines of psychometrics into several other fields including medicine and engineering.