Non-negative Matrix Factorization Algorithms And Applications

With the vigorous development of science and technology,the Internet is also developing rapidly,human beings have been invisibly pushed into the information age.The information age makes people have to face the difficulties and challenges of analyzing and processing large-scale information data.Therefore,the processing of big data becomes particularly important.Low rank approximation of matrix is a method used to approximate large scale information matrix,can effectively achieve dimension reduction of the matrix.Non-negative matrix factorization(NMF)as a newly popular method of low rank approximation of matrix,the basic idea is decompose a given non-negative matrix into a product two low rank non-negative matrices.That is,projecting a high-dimensional non-negative matrix into a low-dimensional subspace.For the traditional NMF method,the represented sample data is based on the whole rather than part,it is usually necessary to mine the essential characteristics of the sample data in the real world.NMF method has a simple decomposition form,the decomposition result is interpretable,and the storage space is also relatively small.Therefore,it is of practical significance and application value to further study the non-negative matrix factorization method.At present,NMF method have been successfully applied in the fields of face recognition,image feature extraction and social network.The non-negative matrix factorization algorithm and its application are studied in this paper.The improved non-negative matrix factorization algorithm based on Newton method and the projection non-negative matrix factorization algorithm based on Newton method are proposed respectively.The iteration rule and detailed calculation process are given,and the program implementation is carried out.The main contents of this paper are as follows:First,this paper describes the research background and significance of non-negative matrix decomposition and the current research situation at home and abroad,and simply describes the development trend of the NMF.Finally,summarizes the main research content and structure of the arrangement.The second chapter mainly introduces the origin,application and related basic theoretical knowledge of non-negative matrix factorization,and describes the existing classical NMF algorithm,gives the algorithm framework,and analyzes the advantages and disadvantages of the algorithm.Based on Newton-based algorithm,an improved non-negative matrix factorization algorithm based on Newton method is proposed.The advantage of this algorithm is that the rank two correction formula is used to replace the inverse calculation of Hessian matrix,and the single-step computation cost is reduced.The algorithm framework is given and the convergence of the algorithm is analyzed.The experiment shows that the algorithm is effective when is applied to ORL face image database.Based on Newton-based algorithm,a projection non-negative matrix factorization algorithm based on Newton method is proposed.Using the knowledge of projection theoryand choosing the appropriate descending direction and step size,the convergence speed of the algorithm is accelerated.The algorithm framework is given and the convergence of the algorithm is analyzed.The experiment shows that the algorithm is effective when it is applied to ORL face image database.