An Efficient Method to Solve Small Sample Size Problem of Nonlinear Discriminant Vectors in Feature Space for Face Recognition

In this paper, we propose an efficient method for solving small sample size problems of nonlinear discriminant vectors (NDVs) in feature space for face recognition via kernel trick. In feature space, the optimal nonlinear discriminant vectors are solved by performing the orthogonalization in the range space of the between class scatter matrix and the range space and null space of the within class scatter matrix. The theoretical justification of the proposed method is presented. Because the orthogonalization is utilized to search NDVs in a larger space compared with the existing methods, the drawback of high computational complexity in the existing methods in the case of the small sample size problem of Generalized Discriminant Analysis (GDA) are successfully overcome. The effectiveness of the proposed method is verified in experiments on the standard face database.