Research On Non-negative Matrix Factorization Algorithm

With the rapid development of artificial intelligence technology, face recognitiontechnology which is widely studied is an important part of the field of biologicalcharacteristics identification. The main purpose of face recognition technology is to extractand classify effective information of face images. At the international level, NMF which israised recently and has been successfully applied to the face recognition is a local featureextraction method. Non-negative matrix factorization is a matrix decomposition thatapproximates a non-negative input matrix by a low-rank approximation composed ofnon-negative factors. It can get an part-based representation of the original high dimensionaldata.This paper studies the basic principle of NMF, and some improved NMF algorithms areclassified, summarized and analyzed. NMF algorithm and many improved NMF algorithmsdo not take into account the intrinsic geometric structure of data and assume that the datadistribution is global linear. It greatly limits the use of NMF algorithm when data is located inthe nonlinear manifold. Compared with the traditional linear dimensionality reductionalgorithms, manifold learning algorithms can reveal the intrinsic geometric structure of dataand look for isometric embedding of the high dimensional data in a low dimensional space inorder to improve the recognition rate. A method called Graph Regularized Non-negativeMatrix Factorization with Sparseness Constraints（GNMFSC）is proposed for enhancing theclassification accuracy. It combines GNMF with NNSC precenting an new algorithm, whichnot only considers the geometric structure in the data representation, but also introducessparseness constraint to coefficient matrix and integrates them into one single objectivefunction.Experiments on ORL and MIT-CBCL face database demonstrate that GNMFSC iscompared with other improved NMF algorithms. The results indicate that the GNMFSCalgorithm can obtain better sparse matrix image, fast convergence speed and high recognitionrate.