On the Iterative Proportional Fitting Procedure: Structure of Accumulation Points and L1-Error Analysis
- A new analysis of the Iterative Proportional Fitting procedure is presented. The input data consist of a nonnegative matrix, and of row and column marginals. The output sought is a biproportional fit, that is, a scaling of the input matrix by means of row and column divisors so that the scaled matrix has row and column sums equal to the input marginals. The IPF procedure is an algorithm alternating between the fitting of rows and columns. The structure of its accumulation points is explored in detail. The progress of the algorithm is evaluated through an L1-error function measuring the deviation of current row and column sums from target marginals. A formula is obtained, of max-flow min-cut type, to calculate the minimum L1-error directly from the input data. If the minimum L1-error is zero, the IPF procedure converges to the unique biproportional fit. Otherwise, it eventually oscillates between various accumulation points.
