  As we all known, the nonnegative matrix factorization (NMF) is a dimension
reduction method that has been widely used in image processing, text
compressing and signal processing etc. In this paper, an algorithm for
nonnegative matrix approximation is proposed. This method mainly bases on the
active set and the quasi-Newton type algorithm, by using the symmetric rank-one
and negative curvature direction technologies to approximate the Hessian
matrix. Our method improves the recent results of those methods in [Pattern
Recognition, 45(2012)3557-3565; SIAM J. Sci. Comput., 33(6)(2011)3261-3281;
Neural Computation, 19(10)(2007)2756-2779, etc.]. Moreover, the object function
decreases faster than many other NMF methods. In addition, some numerical
experiments are presented in the synthetic data, imaging processing and text
clustering. By comparing with the other six nonnegative matrix approximation
methods, our experiments confirm to our analysis.
