Alternating direction method for approximating smooth feature vectors in Nonnegative Matrix Factorization

In many applications of Nonnegative Matrix Factorization (NMF), the features vectors can be approximated by linear combinations of some basis functions that reflect the prior knowledge on the estimated factors. This approach is useful for modeling smoothness or unimodality. However, to estimate the coefficients of these linear combinations, a large-scale QP problem needs to be formulated and solved in each alternating optimization step. To alleviate a huge computational complexity of this approach, we applied the fast alternating direction method of multipliers to our model. As a result, our algorithm outperforms the well-known NMF algorithms in terms of efficiency for solving linear spectral unmixing problems.