A Weighted Procrustes Criterion

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Abstract
The Procrustes criterion is a common measure for the distance between two matrices X and Y, and can be interpreted as the sum of squares of the Euclidean distances between their respective column vectors. Often a weighted Procrustes criterion, using, for example, a weighted sum of the squared distances between the column vectors, is called for. This paper describes and analyzes the performance of an algorithm for rotating a matrix X such that the column-weighted Procrustes distance to Y is minimized. The problem of rotating X into Y such that an aggregate measure of Tucker's coefficient of congruence is maximized is also discussed.