A command that rotates the selected Configuration object to a new Configuration object whose coordinates have maximum squared variance.
The iteration process stops when either the maximum number of iterations is reached or the tolerance criterion is met, which ever one is first.
The Varimax rotation procedure was first proposed by Kaiser (1958). Given a numberOfPoints × numberOfDimensions configuration A, the procedure tries to find an orthonormal rotation matrix T such that the sum of variances of the columns of B*B is a maximum, where B = AT and * is the element wise (Hadamard) product of matrices. A direct solution for the optimal T is not available, except for the case when numberOfDimensions equals two. Kaiser suggested an iterative algorithm based on planar rotations, i.e., alternate rotations of all pairs of columns of A.
However, this procedure is not without problems: the varimax function may have stationary points that are not even local maxima. We have incorporated an algorithm of Ten Berge (1995) that prevents this unpleasant situation from happening.
© djmw, April 7, 2004