Research On Face Recognition Algorithm Based On Fractional Inner Product Kernel Non-negative Matrix Factorization

It is known that biometric technologies have shown their potential applications in the real world.As one of the biometric technologies,face recognition technology is the most widely accepted biometric method because it is non-mandatory,non-contact and safe,and it plays a very important role in the fields of national security,social economy and other fields.The key to face recognition technology lies in feature extraction.Non-negative matrix factorization(NMF)is an effective method to extract non-negative features of facial images.However,the classical NMF method is only a linear feature extraction method and has undesirable performance on facial mage data,which is often nonlinearly distributed because of variations of pose and illuminations etc.The NMF method based on the kernel method,such as the kernel non-negative matrix factorization using polynomial kernel(PNMF,PKNMF,etc.),can effectively overcome the nonlinear problem of face recognition,but they still encounter the following problems:(1)the polynomial kernel function can only take a positive integer power It greatly limits the selection range of the optimal kernel parameters;(2)the loss functions of these algorithms exploit Frobenius norm,but F-norm is sensitive to outliers;(3)slow convergence problem;(4)non-sparse problem in nonnegative feature space.In order to deal with above-mentioned problems,this dissertation has carried out in-depth research on face recognition algorithms based on non-negative matrix factorization(NMF)and has obtained the following innovative achievementsFor the problem that the power exponential parameter of the polynomial kernel function can only take a positive integer,the third chapter first constructs a new fractional power inner product function,and theoretically proves it to be a new Mercer kernel function.In particular,the power exponent of the kernel function can take any non-negative real number,and the kernel function contains more data information than the polynomial kernel function in the power exponent 0<d<1,which greatly expands the selection range of the optimal kernel parameter and lays a foundation for developing a high-performance kernel non-negative matrix factorization algorithmBased on the self-constructed fractional inner product Mercer kernel function,the third chapter further proposes a new nonlinear kernel non-negative matrix factorization method.By using gradient descent method to solve two convex optimization problems,the iterative formulae of the self-constructed fractional inner product Mercer kernel non-negative matrix factorization(FKNMF)algorithm are obtained.Compared with the kernel non-negative matrix factorization algorithms based on polynomial kernel function(PNMF and PKNMF),experimental results indicate that the proposed FKNMF algorithm achieves superior performance in both convergence speed and face recognitionBased on the self-constructed fractional power inner product Mercer kernel function,the fourth chapter presents a novel exponential gradient fractional power inner product kernel non-negative matrix factorization(EFKNMF)algorithm.We solve two sub-optimization problems using gradient descent and exponential gradient descent strategies respectively and derive out the iterative formulae of the EFKNMF algorithm.The convergence of EFKNMF algorithm is theoretically shown by constructing the auxiliary function of the objective function.In the experiments,it is verified that EFKNMF algorithm outperforms FKNMF algorithm and some state of the art algorithmsChapter 5 proposes a new nonlinear NMF method for face recognition.We first establish the objective function in fractional power inner product kernel space.The objective function contains one error term with l2,p norm and one feature sparse regularization term.The l2,p norm is used to solve the outlier problem of the data.Based on the self-constructed fractional power inner product Mercer kernel function,and gradient descent method and its exponential generalization,a sparse fractional power inner product kernel non-negative matrix factorization(FKNMF)algorithm is acquired.The algorithm is theoretically proven to be convergence by means of the constructed auxiliary function.In the noisy and noiseless experiments,the FKNMF algorithm has high discriminative power and accuracy in face recognition.