Research On Feature Extraction Algorithms And Face Recognition In The Case Of Small Sample Size Problem

In face recognition tasks, the number of samples of the training face images is often smaller than that of the dimension of the face images. This problem is so called small sample size (SSS) problem. The SSS problem can cause the ill-posed problem in Rayleigh-based feature extraction algorithms, and influence the generalization capability of classifiers. The dissertation focuses on the face image feature extraction and recognition in case of SSS problem and some researches have been done.The major research works in the dissertation include the following several aspects:(1) In order to overcome the SSS problem encountered by the discriminant locality preserving projections (DLPP) algorithms, a new discriminant locality preserving projections based on maximum margin criterion (DLPP/MMC), which is motivated by the idea of maximum margin criterion (MMC), is proposed. The objective of DLPP/MMC is based on the difference, rather than the Rayleigh ratio. Besides, an efficient and stable algorithm for implementing DLPP/MMC is also proposed. DLPP/MMC can avoid the inverse matrix operation and the SSS problem. Theoretical analysis of DLPP/MMC shows that DLPP/MMC can derive its discriminant vectors from both the range of the locality preserving between-class scatter and the range space of locality preserving within-class scatter. DLPP/MMC can also derive its discriminant vectors from the null space of locality preserving within-class scatter when the parameter of DLPP/MMC approaches+∞.(2) Three improved discriminant locality preserving projections algorithms, i.e. orthogonal complete discriminant locality preserving projections (OCDLPP), regularized generalized discriminant locality preserving projections (RGDLPP) and fast complete discriminant locality preserving projections (FCDLPP). are proposed.In order to design the OCDLPP algorithm, firstly, the locality preserving within-class scatter is replaced by the locality preserving total scatter. Then, the dimension of all the training samples is reduced by removing the null space of the locality preserving total scatter. Finally, the discriminant vectors of the OCDLPP are orthogonalized to improve the discriminant abiltily further. The relations among all kinds of orthogonal schemes are also discussed in the dissertation.RGDLPP also reduces the dimension of all the training samples by removing the null space of the localty preserving total scatter. Then RGDLPP regularizes the eigenvalues of locality preserving within-class scatter. Finally, the optimal discriminant projection matrix is obtained by using the generalized eigenvalue decomposition.The complete discrimant locality preserving projections (CDLPP) has two problems, i.e. the computation complexity is high and the regular discriminant features and the irregular discriminant features do not effectively fused. To address the problems of CDLPP, a fast complete discriminant locality preserving projections (FCDLPP) is proposed. There is only one step of economic QR factorization for FCDLPP algorithm to obtain the optimal discriminant vectors in the null space of locality preserving within-class scatter. Then one step of eigen-decomposition is used to obtain the optimal discriminant vectors in the principal space of the locality preserving within-class scatter. Comparing to CDLPP, the computation complexity of FCDLPP is much lower than that of CDLPP, and then FCDLPP is much faster than CDLPP. Besides, FCDLPP fuses the regular discriminant features in the principal space and irregular discriminant features in the null space, and then the recognition rate of FCDLPP is higher than that of CDLPP.(3) The theoretical analysis on all kinds of kernel approaches interpreted in kernel extension of graph embedding (KGE) is given and the essence of KGE is revealed, i.e. KPCA plus all kinds of linear dimension reduction approaches interpreted in linear extension of graph embedding (LGE). This formalization provides us with a new viewpoint of the kernel-based algorithms. The kernel-based algorithms themselves become more intuitive, more understandable and easier to be implemented. Besides, based on the theory framework, some complete kernel algorithms which take advantage of the discriminant feature in both null and non-null spaces are developed and our proposed complete approaches can get higer recognition rates than the original ones.(4) Facial feature extraction method based on sparse representation is studied, and then a new supervised facial feature extraction algorithm named discriminant sparsity neighborhood preserving embedding (DSNPE) is proposed. DSNPE uses the sparse representation to construct the within-neighborhood graph and between-neighborhood graph, and then the neighborhood parameter can be determined by sparse representation automatically instead of artificially predefined. Finally, the objective function of DSNPE is defined by using the maximum margin criterion. The experiment results on some real face databases demonstrate the effectiveness of the proposed DSNPE algorithm.