Research On Face Recognition Algorithm Based On Non-Negative Matrix Factorization

Face recognition technology plays an important role in people life,while it is key for face recognition to extract feature.Non-negative Matrix Factorization(NMF)is an effective algorithm for face recognition and can extract non-negative features of facial pattern.Because facial image is effected from some factors,such as illumination,pose and occlusion,distribution of its data is complex and nonlinear,in this case,NMF fails.Meantime,NMF doesn't utilize label information,namely it is an unsupervised method,which weakens its classification ability.In addition,NMF's convergence rate and feature sparseness can be further enhanced.Finally,NMF can't perform incremental learning,in other words,when new samples or classes are available,NMF must be repeatedly performed on original training samples,which is very time-consuming.For above mentioned NMF's problems,in this dissertation,we research face recognition algorithms based on NMF in depth.This dissertation includes five chapters.The first chapter introduces background and typical algorithms on face recognition.Main studying work are given in chapter 2 to chapter 4.The last chapter makes the conclusion and discusses future work.To improve further NMF's convergence rate and recognition performance,based on two kinds of different error measurements,namely Euclidean distance and Kullback-Leibler divergence,the second chapter proposes two kinds of Fast Non-negative Matrix Factorization(FNMF),respectively.In non-negativity condition,FNMF suitably chooses larger iterative step-length in the gradient descent method than that of NMF,which improves convergence rate of NMF algorithm and extracts more accurate features.It is proven that NMF is the special case of FNMF.To enhance discriminant power of non-negative features,we develop also two kinds of Block Fast Non-negative Matrix Factorization(BFNMF)by adopting block technique into FNMF.BFNMF is a linear and supervised algorithm and has some merits,such as highly sparse features and orthogonal features from different classes.Experiment testifies that FNMF has faster convergence rate than that of NMF.Experiments for face recognition onORL,FERET,pain expression(PE)and CUM PIE databases demonstrate that BFNMF achieve excellent performance and FNMF achieve better performance than that of NMF.The third chapter proposes the Block Kernel Non-negative Matrix Factorization(BKNMF)which is a nonlinear and supervised method.By utilizing discriminant information of each class,we firstly construct a novel objective function which aims to reduce the within-class distance.Based on kernel theory,the iterative formulas of BKNMF can be obtained by minimizing objective function.Finally,BKNMF can be developed by employing the block strategy,and applied successfully to face recognition.We theoretically give the proof of convergence of BKNMF.BKNMF not only improve discriminant power of NMF's non-negative features,but also extract effectively nonlinear features of facial pattern.Experiments on ORL,PE and Yale databases manifest BKNMF algorithm achieve satisfied performance on face recognition.The fourth chapter proposes an incremental learning algorithm based on Block Sparse Non-negative Matrix Factorization(BSKNMF).In BSKNMF,firstly a novel objective function is constructed by incorporating sparse term and utilizing discriminant information.Based on the objective function and kernel theory,BSKNMF can be obtained by employing block strategy.Finally,based on BSKNMF,incremental learning algorithm is designed and applied successfully to face recognition.BSKNMF not only extracts more sparse and discriminant features than that of BKNMF,but also its features from different classes are orthogonal.We also analyze theoretically convergence of BSKNMF.In addition,when new samples or classes are available,our algorithm avoids repeatedly training study on original training samples,which enhances dramatically time efficiency.Experiments on ORL and Yale databases demonstrate that our algorithm achieves superior performance on recognition.