  In this paper we generalize the canonical positive scaling of rows and
columns of a matrix to the scaling of selected-rank subtensors of an arbitrary
tensor. We expect our results and framework will prove useful for sparse-tensor
completion required for generalizations of the recommender system problem
beyond a matrix of user-product ratings to multidimensional arrays involving
coordinates based both on user attributes (e.g., age, gender, geographical
location, etc.) and product/item attributes (e.g., price, size, weight, etc.).
