A Sampling Algorithm to Compute the Set of Feasible Solutions for NonNegative Matrix Factorization with an Arbitrary Rank

Nonnegative matrix factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern that NMF can result in nonunique solutions. Often, there exist set of feasible solutions (SFS), which makes it more difficult interpret the factorization. This problem especially ignored cancer genomics, where used infer information about mutational processes present evolution cancer. In this paper extent nonuniqueness investigated for two counts new sampling algorithm find SFS introduced. Our easy implement applies arbitrary rank NMF. contrast state art, must be smaller than or equal four. For lower ranks we show our performs similar polygon inflation developed relation chemometrics. Furthermore, how size have high influence on appearing variability solution. implemented R package (https://github.com/ragnhildlaursen/SFS).