Non-negative Matrix Factorization And Its Applications To Face Recognition

Non-negative Matrix Factorization (NMF)is a recent powerful matrix decomposition technique that approximates a non-negative input matrix by a low-rank approximation composed of non-negative factors.It has found wide applicability across a broad spectrum fields,ranging from problems in face recognition,text analysis,and gene microarray analysis,to music transcription. However, Most NMF algorithms suffer from lack of convergence,and when they converge, are notoriously slow to converge.In particular, when applied to face recognition,NMF gives poor recognition performance.In short,the major contributions of this thesis are summarized as follow:1.This thesis explores ANLSPG-NMF (Alternating Nonnegative Least Squares using Projected Gradient with Armijo Rule for NMF) algorithm.While the popular Lee and Seung's multiplicative update method still lacks convergence results, ANLSPG-NMF algorithm exhibits nice optimization properties.However, ANLSPG-NMF algorithm converges slower than the Lee and Seung's multiplicative update method.When used for computing NMF, ANLSPG-NMF algorithm calls projected gradient with Armijo rule per iteration for solving two non-negative constrained linear least squares problems.Selecting the step size a is the most time consuming operation in the projected gradient with Armijo rule.A new strategy for selecting the step size a is introduced.A modified ANLSPG-NMF algorithm is proposed.The experimental result shows that the modified ANLSPG-NMF algorithm converges faster than the ANLSPG-NMF algorithm.This new method is thus an attractive approach to computing NMF.2.This thesis also explores a weighted modification of Fisher Non-negative Matrix Factorization (FNMF) algorithm for face recognition.Inspired by the fact that Eyes, mouth and nose have been determined to be important for face perception and recognition and these features are approximately located in the center of a face,a feature extraction method should give more importance to the central area of each face of training image set. A weighted modification of FNMF for improving FNMF-based face recogniton performance is proposed by introducing a weight matrix at the cost function of the FNMF decomposition.The experimental result also supports the conclusion that the new algorithm can achieve a better performance in face recognition.