Face Image Feature Extraction And Recognition In The Case Of Small Sample Size Problem

In face recognition tasks, the number of samples of face image is commonly smaller than the number of the original facial features. This problem is so called small sample size (SSS) problem. The SSS problem can cause the ill-posed problem in Fisher discriminant analysis for facial feature extraction, and influence the generalization capability of classifiers. This paper focuses on the face image feature extraction and recognition in the case of SSS problem. The main contributions are summarized as follows:1. The problems in ICA-based face recognition are analyzed, and kernel principal component analysis (KPCA) based optimal discriminant independent component analysis (ICA) is proposed. First, the ICA is performed in KPCA transformed space, which reduces the computational complexity and improve the convergence in ICA. Second, the Fisher discriminant information is defined to select the optimal discriminative independent components. Third, an approach is proposed to obtain the optimal feature of unknown sample using the selected optimal discriminative independent component. The experimental results show that this method can achieve better performance than Fisherface method.2. The equivalence between canonical correlation analysis (CCA)and Fisher linear discriminant analysis (FLDA) is first proofed briefly. Then three methods of facial features extraction are proposed based on CCA. (1) In PCA+CCA method, the samples are firstly projected onto the range space of the total scatter matrix, and then CCA is performed to extract optimal discriminant features without losing any discriminatory information. (2) In KPCA+CCA method, CCA is performed in KPCA transformed space to extract the nonlinear optimal Fisher discriminative features of face image, which is equivalent to the kernel Fisher discriminant analysis (KFDA) in nature due to the equivalence between KFDA and KPCA+LDA. (3) CCA is directly extended to kernel based CCA, which is also equivalent to KFDA due to the equivalency between CCA and FLDA. The experimental results show that three methods significantly outperform Fisherface and KPCA+LDA methods.3. The discriminative common vectors method (DCV) successfully overcomes the drawbacks of existing method for solving the SSS problem of FLDA in face recognition. However DCV is linear technique in nature. In this paper, the KDCV is proposed by combining the DCV and kernel method to extract the nonlinear Fisher discriminative features. The Gram-Schmidt orthogonalization procedure in feature space is first presented, which is equivalent to performing a Cholesky decomposition of kernel matrix. Then the algorithm for KDCV is developed by performing the Gram-Schmidt orthogonalization twice in feature space, which is equivalent to computing two kernel matrices and performing a Cholesky decomposition of kernel matrix. The experiment indicates that KDCV achieve better performance than DCV. 4. The kernel based nearest feature classifiers (KNFC) are proposed, which can directly classify the high dimensional face images without the preprocessing step to extract the facial features. Therefore, in the case of large number of training samples, the problem of high computational cost for facial features extraction can be avoided. Two KNFS methods are presented. One is the direct generalization of KNFP and the other utilizes KPCA to construct the nonlinear feature subspace for each face class. To solve the problem of the large computational complexity and...