  Nonnegative matrix factorization has been widely applied in face recognition,
text mining, as well as spectral analysis. This paper proposes an alternating
proximal gradient method for solving this problem. With a uniformly positive
lower bound assumption on the iterates, any limit point can be proved to
satisfy the first-order optimality conditions. A Nesterov-type extrapolation
technique is then applied to accelerate the algorithm. Though this technique is
at first used for convex program, it turns out to work very well for the
non-convex nonnegative matrix factorization problem. Extensive numerical
experiments illustrate the efficiency of the alternating proximal gradient
method and the accleration technique. Especially for real data tests, the
accelerated method reveals high superiority to state-of-the-art algorithms in
speed with comparable solution qualities.
