Research On Non-negative Matrix Factorization With Manifold Structure For Face Recognition

Feature extraction is one of the most crucial stages in face recognition.Nonnegative matrix factorization(NMF)has the capability of extracting nonnegative sparse features of facial images because the decomposition is under the nonnegative constraint.It is known that the facial image data maybe nonlinearly distribute in the pattern space,and also reside on a manifold embedded in a low dimensional feature space due to the variations of illumination,pose and facial expression.However,NMF lacks the ability of modeling the structure of data manifold,which contains important local and nonlocal features for data classification.Meanwhile,NMF is an unsupervised learning approach since it is implemented without utilizing the labels of the training data.Furthermore,NMF is a linear feature extraction scheme and thus cannot deal with the nonlinear problem of face recognition.These mentioned problems will degrade the performance of traditional NMF algorithm.To overcome the limitations of NMF,this dissertation carries out an in-depth study on NMF algorithm and presents three novel NMF-based approaches.The proposed algorithms are successfully applied to face recognition and achieve better performances.This dissertation involves five chapters.The first chapter briefly introduces the background and the related algorithms on face recognition.Our main research findings are given in Chapter 2 to Chapter 4.The last Chapter 5 draws the conclusions and discusses the future work.The second chapter proposes a novel nonnegative matrix factorization algorithm with manifold structure(Mani-NMF).In order to make the data in the same manifold as close as possible and the data between different manifolds as far as possible,two quantities related to adjacent graph and non-adjacent graph are incorporated into the objective function,which will be minimized by solving two convex sub-optimization problems.Based on gradient descent method and auxiliary function technique,we acquire the update rules of Mani-NMF and theoretically prove that the objective function is monotonic non-increasing under the iterations.Three publicly available face databases,namely Yale,pain expression databasesand CMU Face Images,are selected for evaluations.Experimental results indicate that our algorithm outperforms the other algorithms.To tackle the nonlinear problem of face recognition,Chapter 3 proposes a novel nonlinear nonnegative matrix factorization method,called local and nonlocal feature based kernel NMF(LN-KNMF)method.We nonlinearly map the samples into a high dimensional kernel space and establish a objective function with manifold structure in the kernel space.We obtain the iterative formulas of LN-KNMF algorithm using polynomial kernel and gradient descent method,and then show the convergence of the proposed LN-KNMF algorithm.Experimental results on the ORL,Yale and FERET databases demonstrate the superior performance of our approach against some NMF-based methods.To enhance the discriminative power of NMF algorithm in kernel space,Chapter 4present a novel adjacent graph based Block Kernel NMF(AG-BKNMF)algorithm,which is a supervised learning method.Based on the class label and local scatter information,we construct a new objective function in kernel space.The local scatter quantity is defined by the local adjacent graph,while the class label information is embodied in both block technique and within-class scatter matrix.Subsequently,We theoretically construct an auxiliary function related to the objective function and then derive the iterative formulas of our method by solving the stable point of the auxiliary function.The property of auxiliary function shows that our algorithm is convergent.Finally,empirical results show that our method is effective on face recognition.