Face recognition using extended generalized Rayleigh quotient

Generalized Rayleigh quotient is a powerful mathematical tool. This framework can combine two conflicting objectives, the maximization and minimization, in one unified function. Many problems in machine learning can be considered as the optimization of generalized Rayleigh quotient. In this paper, we propose an extension of generalized Rayleigh quotient framework and develop a new method for face recognition based on this framework. This method minimizes the residual of within-class collaborative representation and maximizes the residual of between-class collaborative representation. Then intra-class and inter-class adjacency graphs are constructed as constraints imposed on the two residuals respectively to preserve the consistency of distance property. Solution is iteratively obtained from generalized eigenvalue problem. The proposed method is evaluated on benchmark face databases and outperforms other state-of-the-art methods.