Least-Squares Methods for Nonnegative Matrix Factorization Over Rational Functions

Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings continuous signals, factors in NMF can be constrained samples rational functions, which allow fairly general models; this referred as using functions (R-NMF). We first show that, under mild assumptions, R-NMF has an essentially unique factorization unlike NMF, crucial applications where ground-truth need recovered such blind source separation problems. Then we present different approaches solve R-NMF: R-HANLS, R-ANLS and R-NLS methods. From our tests, no method significantly outperforms others, a trade-off should done between time accuracy. Indeed, R-HANLS fast accurate for large problems, while more accurate, but also resources demanding, both memory. very only small Moreover, that various tasks including recovery semi-synthetic classification problem real hyperspectral signals.