Considerations on Parallelizing Nonnegative Matrix Factorization for Hyperspectral Data Unmixing

Nonnegative matrix factorization (NMF) is a recently developed linear unmixing technique that assumes that the original sources and transform were positively defined. Given that the linear mixing model (LMM) for hyperspectral data requires positive endmembers and abundances, with only minor modifications, NMF can be used to solve LMM. Traditionally, NMF solutions include an iterative process resulting in considerable execution times. In this letter, we provide two novel algorithms aimed at speeding the NMF through parallel processing: the first based on the traditional multiplicative solution and the second modifying an adaptive projected gradient technique known to provide better convergence. The algorithms' implementations were tested on various data sets; the results suggest that a significant speedup can be achieved without decrease in accuracy. This supports the further use of NMF for linear unmixing.