Modified Generalized Discriminant Analysis Using Kernel Gram-Schmidt Orthogonalization in Difference Space for Face Recognition

In this paper, we propose an efficient method to compute the optimal discriminant vectors of Generalized Discriminant Analysis (GDA) for face recognition tasks. The optimal discriminative features of face images are obtained by directly performing the kernel Gram-Schmidt orthogonalization procedure on the difference vectors only once. The theoretical justification is presented. The nonlinear difference vectors are first expressed using data matrix and two transformation matrices. Then, the Cholesky decomposition is performed on a kernel matrix which is obtained using data matrix and two transformation matrices. Since the proposed method does not apply the singular value decomposition as does in the traditional GDA, the high numerical stability is achieved. Moreover, because there is no need to compute the mean of classes and the mean of total samples in the proposed method, the computational complexity is reduced greatly. The effectiveness of the proposed method is verified in the experiments on two standard face databases.