Adaptive Data-dependent Matrix Norm Based Gaussian Kernel for facial feature extraction

In this paper, we propose a novel kernel named Adaptive Data-dependent Matrix Norm Based Gaussian Kernel (ADM-Gaussian kernel) for facial feature extraction. As a popular facial feature extraction method for face recognition, the current kernel method endures some problems. Firstly, the face image must be transformed to the vector which leads to the large storage requirements and the large computational effort, and secondly since the different geometrical structures lead to the different class discrimination of the data in the feature space, the performance of the kernel method is influenced when kernels are inappropriately selected. In order to solve these problems, firstly we Create a novel matrix norm based Gaussian kernel which views images as matrices for facial feature extraction, which is the basic kernel for the data-dependent kernel. Secondly we apply a novel maximum margin criterion to seek the adaptive expansion coefficients of the data-dependent kernel, which leads to the largest class discrimination of the data in the feature space. Experiments on ORL and Yale databases demonstrate the effectiveness of the proposed algorithm.