The Research Of Non-negative Matrix Factorization Algorithm

With advances in science and technology, the scope of the study has been observed more and more widely, the need to analyze the size of the data processing becoming bigger and bigger, how to effectively analyze these large amounts of data, and to extract useful information has become very important. Non-negative matrix factorization i.e. NMF of low rank approximation can solve these problem. At present, NMF algorithm has been successfully extended to the real life, such as face recognition, text analysis and so on.According to the square of the Euclidean distance defines the objective function of NMF, based on alternating least squares method i.e. ANLS method, NMF can be converted into a class of optimization problems with constraints. But some better algorithms of unconstrained optimization problems, such as Barzilai-Borwein algorithm i.e. BB algorithm, conjugate gradient method i.e. CG method, how to be applied to the NMF. The paper obtains from the problem, studied the algorithm of NMF, and the main research works are:First of all, due to the BB algorithm cannot be applied directly to the NMF algorithm, this paper combined it with an active set algorithms i.e. AS algorithm, and then proposed an active set BB algorithm. The algorithm defines a new active set, and uses a nonmonotone linesearch technique. The convergence analysis shows that the algorithm can converge to a stationary point, compared with classical projected gradient algorithm i.e. PG algorithm is verified the algorithm not only numerical effect is better, but also through the recognition of experiments, the effect is more obvious image.Secondly, combining the LS conjugate gradient method with the AS algorithm, this paper puts forward an active set LS conjugate gradient method i.e. ALS method, that is, to promote the CG method to the NMF. By analyzing the convergence of ALS method shows that this method is feasible, and comparing with PG algorithm, alternating projection Barzilai-Borwein algorithm i.e. APBB algorithm in numerical experiments and simulation, shows the ALS algorithm has better results.