Non-negative Matrix Factorization And Its Applications

In today’s rapid development of science and technology, the data processing problem hasbecome one of the significance topic studied by scientists. Non-negative Matrix Factorization(NMF)to solve the issues of large amounts of data processing.The main purpose of facerecognition technology is to extract of face images. Compared with other subspace learningmet hods The NMF algorithm at first introduce the nonnegative constraint matrixdecomposition process.It can get an part-based representation That would reaction the localcharacteristics of the original data.This paper studies the basic principle of NMF, and some improved NMF algorithmsapplied to the face feature extraction.Compared with traditional Non-negative MatrixFactorization with Projective has the advantafes of dimension reduce and save NMFcomputing time.Because the NMF algorithm and its improved algorithm using The originaldata is linear manifold, It infinitely limits the use of NMF algorithm when data is located inthe nonlinear manifold So add near the figure matrix in the sample data retention of geometricintrinsic structure at the same time, and get more effective coefficient matrix.In this paper,based on NMF and some improved NMF, advances and studied a new improved ofnonnegative matrix factorization algorithm.A method called Graph Regularized Non-negativeMatrix Factorization with Projective (PGNMF). This algorithm with Kullback-Leiberdivergence.KL divergence is a very popular measurement in machine learning and datamining.And we propose a multiplicative updates for PGNMF with KL divergence.Experimental results demonstrate that the bases derived by PGNMF with KL divergence aresomewhat better suitable for a localized and sparse representation than the bases by thetraditional NMF, as well as being more orthogonal.Experiments on ORL and MIT-CBCL face database demonstrate that PGNMF iscompared with other improved NMF algorithms. The results indicate that the PGNMFalgorithm can obtain better sparse matrix image, fast convergence speed and high recognitionrate.