  Non-negative signals form an important class of sparse signals. Many
algorithms have already beenproposed to recover such non-negative
representations, where greedy and convex relaxed algorithms are among the most
popular methods. One fast implementation is the FNNOMP algorithm that updates
the non-negative coefficients in an iterative manner. Even though FNNOMP is a
good approach when working on libraries of small size, the operational time of
the algorithm grows significantly when the size of the library is large. This
is mainly due to the selection step of the algorithm that relies on matrix
vector multiplications. We here introduce the Embedded Nearest Neighbor (E-NN)
algorithm which accelerates the search over large datasets while it is
guaranteed to find the most correlated atoms. We then replace the selection
step of FNNOMP by E-NN. Furthermore we introduce the Update Nearest Neighbor
(U-NN) at the look up table of FNNOMP in order to assure the non-negativity
criteria of FNNOMP. The results indicate that the proposed methodology can
accelerate FNNOMP with a factor 4 on a real dataset of Raman Spectra and with a
factor of 22 on a synthetic dataset.
