A GENERAL-SOLUTION OF THE WEIGHTED ORTHONORMAL PROCRUSTES PROBLEM

A general solution for the weighted orthonormal Procrustes problem is offered in terms of the least squares criterion. For the two-dimensional case, this solution always gives the global minimum; for the general case, an algorithm is proposed that must converge, although not necessarily to the global minimum. In general, the algorithm yields a solution for the problem of how to fit one matrix to another under the condition that the dimensions of the latter matrix first are allowed to be transformed orthonormally and then weighted differentially, which is the task encountered in fitting analogues of the IDIOSCAL and INDSCAL models to a set of configurations.