Study On Face Recognition Algorithms Based On Nonlinear Subspace Learning And Discriminant Analysis

Face recognition(FR)has been widely used in finance,public security and traffic etc.In practice,it is difficult to extract the image's feature due to the effects of noises,such as expression,illumination,occlusion and low-resolution.Moreover,the human's facial similarity leads to the within-class scatter being greater than between-class scatter,which results in the difficulty for classification.Therefore,improving the quality of feature extraction and discriminant has been a hot topic in FR.Recently,as nonlinear subspace learning,manifold learning and sparse learning methods have been used to discoven the intrinsic structure of face images to improve the quality of feature extraction.To further improve the discriminant of face images,we propose several new FR algorithms in this thesis.The main research works were shown as follows:1.Since the construction of local adjacent matrix in local preserving projection algorithm needs optimized parameters before recognition,a sparse local preserving projection(SLPP)algorithm is proposed.SLPP adopts the relationship between sparse reconstruction coefficients and local adjacent weights,and represents the adjacent weights using the normalized sparse reconstruction coefficients which are computed by sparse representation method and parameter-free,to construct the sparse adjacent structure of samples.However,the local adjacent matrix is symmetrical,whereas sparse adjacent matrix usually asymmetrical.We give a method to preserve asymmetrical manifold structure by algebra derivation.To improve the discriminant of samples,a new algorithm named sparse locality preserving discriminant projection(SLPDP)is proposed.SLPDP can preserve the sparse adjacent structure of samples and,simultaneously,maximize the average margin distance of between-class.Experiments were done on several public face image databases,and the results demonstrated the effectiveness of the proposed algorithms.2.Some existing FR algorithms cannot preserve the within-class sparse reconstruction structure well when taking the within-class discriminant structure.To address this problem,sparse discriminant preserving projection(SDPP)algorithm and sparse adjacent preserving discriminant embedding(SNPDE)algorithm are proposed.SDPP represents the discriminant information using global between-class scatter matrix,and improves the discriminant of samples by maximizing the between-class scatter when preserving the sparse reconstruction relationship.Since SDPP only takes the between-class scatter into account,which does not affect the within-class structure of samples,it can preserve the sparse reconstruction relationship well.SNPDE "penalizes" the margin samples of each class when preserving the within-class sparse reconstruction relationship to improve the samples;discriminant.Since SNPDE only scatters few marginal samples,it has smallest effects on the sparse reconstruction relationship.Experiments on several public face databases demonstrate the effectiveness of two proposed algorithms.3.In order to improve the robustness of FR algorithms in random noise condition,two regularized algorithms based on regression are proposed:regularized linear regression discriminant embedding(RLRDE)and bilateral two-dimensional matrix regression preserving discriminant embedding(B2DMRPDE).RLRDE,supposing the samples from same class are distributed in a linear space,whereas the samples from different classes are placed in different spaces,constructs the within-class reconstruction matrix and betweenclass reconstruction matrix based on l2-norm measurement.By minimizing the withinclass reconstruction residual and maximizing the between-class reconstruction residual,RLRDE aims to find a feature subspace in which the discriminant of face samples can be improved.Experiments were done on vector-based face image sets,and the results demonstrate the effectiveness of the proposed methods.B2DMRPDE,taking the twodimensional geometry structure of face image into account,supposes the within-class reconstruction residual matrix is low-rank and the between-class reconstruction residual matrix is not low-rank,and constructs the nuclear-norm-based within-class reconstruction matrix and between-class reconstruction matrix.By minimizing the quotient of the within-class reconstruction residual and the between-class reconstruction residual,B2DMRPDE aims to find a low-dimensional subspace in which the samples'discriminant can be improved.Since B2DMRPDE reduces the dimensionality of 2D image from row and column directions,it needs to find two different projection matrices.We give an iterative method to compute the two matrices simultaneously.We also prove the convergence and analyse the time complexity of the iterative method.Experiments on several famous face databases with random noises validate the effectiveness of the proposed algorithm.