Novel Alternating Projected Gradient Method For Nonnegative Matrix Factorization

Nonnegative Matrix Factorization(NMF)is an effective matrix decomposition technique which has been widely used in many fields including image processing,text mining,pattern analysis and so on.In this thesis,we consider numerical methods for computing nonnegative matrix factorization.Solving efficiently nonnegative least squares problems is a key to realize the nonnegative matrix factorization since the nonnegative matrix factorization can be split into a series of nonnegative least squares problems.The following results are obtained.Based on the projection of function gradient,we construct a new search direction,present a new step-size selection strategy,and propose a novel projected gradient method for solving nonnegative least squares problem,and analyze its convergence properties.Applying the developed projected gradient method to the NMF problem,we present a new alternating projected gradient method for computing NMF.Numerical results show that the proposed method is superior to both the multiplicative update algorithm and the projected gradient method for the NMF.