Non-negative Matrix Factorization Based on Projected Nonlinear Conjugate Gradient Algorithm

The popular multiplicative algorithms in non-negative matrix factorization (NMF) are known to have slow convergence. Several algorithms have been proposed to improve the convergence of iterative algorithms in NMF, such as the projected gradient algorithms. However, these algorithms also suffer a common problem, that is, a previously exploited descent direction may be searched again in subsequent iterations which potentially leads to slow convergence of these algorithms. In this paper, we propose a projected non-linear conjugate gradient algorithm using orthogonal searching directions at each iteration which ensures each descent direction is different from others. The algorithm is shown to have better convergence performance as compared with bothmultiplicative algorithms and the projected gradient algorithms.