Research On Non-negative Matrix Factorization With RBF Kernel For Face Recognition

Face recognition technology has become increasingly mature,and its products are widely used in government,military,banking,education,business and other fields.It is well known that face recognition has the advantages of non-mandatory,natural,concurrency,etc.However,face image data is not only the high dimensionality of the model and the shortcomings such as similarity and variability(light conditions,age,and face occlusion).This brings great difficulty to effectively and successfully recognize the face for computers.How to quickly extract features and improve recognition rate has become the focus of researchers.Among many feature extraction and dimension reduction methods,non-negative matrix factorization(NMF)is a linear method that performs bottom rank decomposition on image data matrices under non-negative constraints and can extract non-negative features of face images,especially can effectively extract the local features of the face image.However,the distribution of face image data in the feature space is very complex and often presents a nonlinear distribution.The linear NMF method reduces the recognition performance of face recognition nonlinear problems.But the kernel method is an effective method for dealing with face recognition nonlinear problems.Therefore,in view of the nonlinear problem of face recognition,this dissertation combines the kernel method with the NMF algorithm,and proposes two new non-negative matrix factorization algorithms based on radial basis kernel function(RBF),and which experiment in the face database to achieve good recognition performance.This dissertation is divided into four chapters.The first chapter mainly introduces the face recognition related algorithms and the research background of non-negative matrix factorization;the second chapter and the third chapter are the main results of the dissertation;the fourth chapter is this The summary and outlook of the paper.Based on the kernel method theory,we propose a multiplicative RBF kernel non-negative matrix factorization algorithm(KNMF-PRBF)in Chapter 2.Compared with the polynomial kernel,the multiplicative RBF kernel function can better describe the similarity between data,and has translation invariance and rotation without deformation,but the RBF kernel has a negative exponent,this brings difficulties to the non-negative constraint of the kernel non-negative matrix factorization algorithm.In order to solve this problem,we use Euclidean distance as the error measure to construct the objective function,and transform its minimum optimization problem into two subconvex optimization problems,and then use the gradient descent method and the positive and negative separation techniques respectively to obtain the multiplication update rule of KNMF-PRBF algorithm.By constructing the auxiliary function of the objective function,we further theoretically analyze the convergence of the algorithm.Finally,our KNMF-PRBF algorithm is successfully applied to face recognition.Four common disclosures in FERET,Yale,AR,CMU PIE Numerical experiments on the face database show that the KNMF-PRBF algorithm is superior to other linear and nonlinear face recognition algorithms.In Chapter 3,we propose a additive RBF kernel non-negative matrix factorization algorithm(KNMF-PRBF).Since multiplicative RBF(PRBF)is sensitive to noise,we first construct an additive RBF(SRBF)kernel function that is robust again noise,then the constructed additive RBF kernel function is applied to the kernel non-negative matrix factorization.By using the gradient descent method to solve the minimization objective function,to derive the update iterative formula of KNMF-SRBF algorithm,and the convergence of the algorithm is proved by the the technique of the auxiliary function.In numerical experiments,noise(Gaussian,salt&peper,speckle,white filler)and non-noise experiments were performed on three public face databases of 101,Yale,and ORL.The noise experiment results show that the KNMF-SRBF algorithm has better noise immunity and higher recognition performance than NMF,LNMF,RSNMF,PNMF and other algorithms.In addition,our proposed KNMF-SRBF algorithm also achieved good recognition accuracy in non-noise experiments.Finally,we theoretically analyzed that the additive RBF core is more robust against noise than the multiplicative RBF kernel,which has been verified from experiments.