Research On Robust Non-negative Matrix Factorization Algorithm

With the rapid development of science and technology,human society has entered the information age.The arrival of the information age makes human face the challenge of efficient processing and analysis of large-scale information data.A large number of high-dimensional data generated on the Internet every day usually has important research value.Non-negative matrix factorization(NMF)is widely used in many fields,such as face recognition,robot control,medical research and so on.This method has a good processing effect on high-dimensional data.There are still some deficiencies in the existing NMF,in order to improve the effectiveness of non-negative matrix factorization methods,many scholars have proposed some improved NMF methods,which improve the performance of NMF methods to a certain extent.However,when the data set contains noise,many existing NMF methods still have the problems of poor performance and robustness.Therefore,this thesis will introduce the non-negative matrix factorization method and further research work.The following describes the work of this thesis and its innovation:(1)In this thesis,the knowledge of non-negative matrix factorization method is described in detail,and how to improve the image recognition efficiency and the robustness of NMF method in the case of noise is fully introduced.In addition,this thesis also summarizes some classical image recognition algorithms,and analyzes the recognition performance of the algorithm through simulation experiments.(2)In view of the shortcomings of the existing NMF methods:firstly,the NMF method calculates its low-dimensional representation directly on the high-dimensional original image data set,but in fact,the effective information of the original image data set is often hidden in its low rank structure;secondly,the NMF method also has the disadvantages of noise sensitivity and poor robustness.In order to improve the robustness and interpretability of NMF algorithm,a non-negative low rank matrix factorization algorithm(SGNLMF)for sparse graph regularization is proposed.Through low rank constraints and graph regularization,SGNLMF algorithm makes use of the geometric information and effective low rank structure of the data at the same time.In addition,SGNLMF algorithm also makes sparse constraints on the base matrix,which improves its robustness and interpretability to a certain extent.Through the simulation experiment on the data sets,the algorithm has a certain degree of improvement in recognition effect and robustness compared with the previous algorithm.(3)Based on the non-negative graph embedding algorithm and the idea of low rank constraint,a non-negative low rank graph embedding algorithm(NLGE)is proposed.In this thesis,the iterative rules for solving NLGE algorithm are given,and the convergence of the algorithm is further proved.In order to further verify the effectiveness of the algorithm,we carried out relevant simulation experiments on the data set,and compared the algorithm with other algorithms,the results show that the algorithm has some advantages over other algorithms.(4)On the basis of non-negative low rank graph embedding algorithm,L21 norm is introduced into graph embedding and data reconstruction function,and a non-negative low rank graph embedding algorithm(NLGEL21)based on L21 norm is proposed.A multiplicative iterative formula for NLGEL21 algorithm is given,and its convergence is proved theoretically.Experiments on face database show that NLGEL21 algorithm is effective.