The Filter-trust-region Method About Non-negative Matrix Factorization

The nonnegative matrix factorization(NMF) is a nonnegative decomposition inwhich all the elements in the matrix are nonnegative, and it is of great practicalsignificance. It provides a new way for people to deal with large data. Compared withsome traditional algorithms, it has the simplicity of implementation and the explanatoryof the decomposition form and decomposition results, taking up less storage space andso on. So it is widely used in image processing, network security, etc.Because multiplicative iterative algorithm and its improved algorithms firstsuggested by nonnegative matrix factorization made the objective function down slowlynear the optimal solution. So looking for rapid decomposition algorithm is always thehot issue of the NMF problem. Aiming at this problem, this paper mainly completed thefollowing job.Firstly, this paper summarizes the penalty function method, the trust-region methodand the filter method with which we solve a bound constrained programming. Secondly,this paper improves the filter-trust-region method proposed by Fletcher, apply it to thenon-negative matrix factorization and compared with the traditional non-negativematrix factorization algorithms. Theoretical analysis and numerical experiments showthat our algorithm has high rate of the convergence. Under the suitable conditions weprove the convergence of the algorithm.