Non-negative Matrix Factorization Under The Manifold Regularization Framework

With the development of computer technology and network, face recognition has beenwidely used in many fields. Face recognition has gradually become the main researchquestion of human exploration of artificial intelligence field.The combination of NMF methodand image processing has become an effective method of data dimensionality reduction andfeature extraction in the field of image processing, pattern recognition. To some extentnon-negative constraints of NMF have produced local based and sparse non-negative matrix.Therefore, it objectively provides a mathematical model which uses “calculations”to“express” visual perception process.This article describes the original NMF algorithm and comprehensive analysis of someclassical NMF improved algorithms. when processing data we found that manynon-negative matrix algorithms and improved non-negative matrix algorithm does not takethe intrinsic geometry of the data into account, so that it greatly limits non-negative matrixfactorization algorithm to use when the data is in the nonlinear manifold. To solve thisproblem, in recent years the proposed manifold learning(Manifold Learning, ML)algorithm isable to reveal the intrinsic geometry of the data and look for isometric embedding ofhigh-dimensional data in a low dimensional space. Based on this, we propose a novel basedon manifold regularization of non-smooth non-negative matrix factorization(MRnsNMF)algorithm, which is used to extract features of face images, by building all samples Neighborschart to estimate the geometry of data space, then add it as a regularization term to theobjective function of non-smooth non-negative matrix factorization.Experiments on ORL, Extended YaleB and MIT-CBCL face database demonstrate thatMRnsNMF is compared with other improved NMF algorithms. The results indicate that theMRnsNMF algorithm can obtain better sparsity in based image and encoded image, fastconvergence speed and high recognition rate.