Non-negative Matrix Factorization And Its Application In Multispectrum Signal Processing

Non-negative matrix factorization algorithm has been proposed for nearly 20 years.Due to its special ability to extract part of the characteristics to percei ve the overall intelligent data description,it quickly attracted a large number of scholars and experts to carry out deeper research and analysis.In fact,the research on non-negative matrix factorization has gone far beyond the exploration of mathematic s.The basic theory of non-negative matrix factorization attempts to develop a feasible model for the learning object part.This idea,which uses the part to represent the whole,is exactly an idea based on partial perception that constitutes the overall perception.This is also a kind of “smart” thinking.Due to its many advantages,non-negative matrix factorization algorithms are becoming more and more diverse,more and more mature,and more and more widely used.This paper focuses on non-negative matrix factorization theory,and mainly analyzes and studies the non-negative matrix factorization based on ? divergence and a local smoothness constrained nonnegative matrix factorization with nonlinear convergence rate.The specific arrangement of this paper is as follows: Firstly,this paper introduces the significance of the research on the topic,the research status at home and abroad,and briefly explains the organizational structure of this paper.Secondly,the basic theory of non-negative matrix factorization is introduced in detail,including the mathematical expression of the non-negative matrix factorization model,summary of the discovered features of the non-negative matrix factorization,the details of the above categories of non-negative matrix factorization and some of the conclusions and unresolved issues in this area.Besides,this paper will study the application of non-negative matrix factorization with the ?-divergence in cluster experiments to test its performance.Furthermore,a local smoothing constrained nonnegative matrix algorithm with nonlinear convergence rate is designed.Finally,the research work of this paper is summarized and prospected.The focus of this paper is as follows:A non-negative matrix factorization algorithm based on ?-divergence is introduced.The basic theory of ?-divergence is introduced first.Then the algorithm model and its derivation process are described in detail.Finally,a basic clustering simulation experiment and a document clustering simulation experiment are performed on the algorithm.The experimental results verify that this algorithm is more efficient than other mainstream NMF algorithms and clustering algorithms in document clustering experiments.A local smoothness constrained nonnegative matrix factorization with nonlinear convergence rate for spectral decomposition is designed.This method can be used in spectral signal processing and can be used to solve the spectral decompose problem.Firstly,we prove that the gradient of the cost function of each variable matrix has Lipschitz continuity characteristics,then we construct an approximate function to optimize the cost function.Therefore,our method can implement a faster nonlinear convergence rate than the traditional method.Secondly,the algorithm model and the derivation process of this algorithm are described in detail.Finally,the simulation experiment results demonstrate the advantages of the algorithm in this chapter in solving the spectral decompose method.