Parallel approach to NNMF on multicore architecture

We tackle the parallelization of Non-Negative Matrix Factorization (NNMF), using the Alternating Least Squares and Lee and Seung algorithms, motivated by its use in audio source separation. For the first algorithm, a very suitable technique is the use of active set algorithms for solving several non-negative inequality constraints least squares problems. We have addressed the NNMF for dense matrix on multicore architectures, by organizing these optimization problems for independent columns. Although in the sequential case, the method is not as efficient as the block pivoting variant used by other authors, they are very effective in the parallel case, producing satisfactory results for the type of applications where is to be used. For the Lee and Seung method, we propose a reorganization of the algorithm steps that increases the convergence speed and a parallelization of the solution. The article also includes a theoretical and experimental study of the performance obtained with similar matrices to that which arise in applications that have motivated this work.