  In this article, we study algorithms for nonnegative matrix factorization
(NMF) in various applications involving streaming data. Utilizing the continual
nature of the data, we develop a fast two-stage algorithm for highly efficient
and accurate NMF. In the first stage, an alternating non-negative least squares
(ANLS) framework is used, in combination with active set method with warm-start
strategy for the solution of subproblems. In the second stage, an interior
point method is adopted to accelerate the local convergence. The convergence of
the proposed algorithm is proved. The new algorithm is compared with some
existing algorithms in benchmark tests using both real-world data and synthetic
data. The results demonstrate the advantage of our algorithm in finding
high-precision solutions.
