The Sinkhorn-Knopp Algorithm:Convergence and Applications

As long as a square nonnegative matrix $A$ contains sufficient nonzero elements, the Sinkhorn-Knopp algorithm can be used to balance the matrix, that is, to find a diagonal scaling of $A$ that is doubly stochastic. We relate balancing to problems in traffic flow and describe how balancing algorithms can be used to give a two sided measure of nodes in a graph. We show that with an appropriate modification, the Sinkhorn-Knopp algorithm is a natural candidate for computing the measure on enormous data sets