Tuning parameter selection for nonnegative matrix factorization

Finding low rank nonnegative decomposition of multivariate data has many important applications in signal processing. A standard method is the nonnegative matrix factorization (NMF). In recent years, many algorithm have been proposed for NMF. However, an important problem that has not received as much attention is the selection of the rank of NMF. In this paper we develop a method for selecting the rank of NMF based on the Stein´s unbiased risk estimator (SURE). In simulations we compare the method against crossvalidation. In addition we apply the method for selecting the rank of NMF for high dimensional hyperspectral data.