Convergence properties of an iterative procedure of ipsatizing and standardizing a data matrix,with applications to parafac/candecomp preprocessing

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution. This solution need not be centered row-wise if the limiting point of the interations is a matrix of rank one. The results of the present paper bear directly on several types of preprocessing methods in Parafac/Candecomp.