Updating/downdating the NonNegative Matrix Factorization

The Non-Negative Matrix Factorization (NNMF) is a recent numerical tool that, given a non-negative data matrix, tries to obtain its factorization as the approximate product of two nonnegative matrices. Nowadays, this factorization is being used in many science fields; in some of these fields, real-time computation of the NNMF is required. In some scenarios, all data is not initially available and when new data (as new rows or columns) becomes available the NNMF must be recomputed. Recomputing the whole factorization every time is very costly and not suitable for real time applications. In this paper we propose several algorithms to update the NNMF factorization taking advantage of the previously computed factorizations, with similar error and lower computational cost.