Nonlinear Fisher Discriminant Based Methods For Face Recognition

Face recognition is an important branch of biologic feature identification. Because of its advantages comparing to other biologic features, considerable attention has been paid to face recognition. Now many approaches to face recognition problem have been devised over the years, from the early geometry based methods to statistics based methods. Although linear techniques have been fully developed, they are still inadequate to describe the complexity of real face images because of the illumination, facial expression and pose variation. Hence it's necessary to extend the linear techniques to the nonlinear ones. In this dissertation, the research focuses on kernel Fisher discriminant analysis. The emphasis is on the extension. The primary contributions and original ideas included in this dissertation are summarized below:1. According to the algorithm of kernel Fisher discriminant analysis (KFDA), a concept, named kernel sample set, is introduced. Based on this concept, KFDA is equivalent to performing FLD on kernel sample set. Then the nonlinear algorithm is converted to a linear one. A great deal of research has been done on linear approaches. And the kernel sample set extends the linear methods to nonlinear ones that can improve the result.2. Two enhanced kernel Fisher discriminant models (EKFD-1 and EKFD-2) are proposed which use a strong combination of enhanced FLD and kernel tricks. It takes the over-fitting dilemma into account, and diagonalizes the within class and between class scatter matrix simultaneously. The result shows that it improves the generalization ability of FLD and EFM.3. Combination with MCA, minor component based kernel fisher discriminant analysis (MKFDA) is proposed. Firstly descend the dimension of the kernel sample set by PCA, then project the data into the MCA space of within-class scatter matrix and perform FLD. The minor components improve the performance of Fisher discriminant, because they contain the difference of each class. The experiment results prove that MKFDA outperforms KFDA and null-space based KFDA algorithm.