Reciprocal kernel-based weighted collaborative-competitive representation for robust face recognition

The Gaussian kernel function is widely used to encode the nonlinear correlations of the face images. However, some issues greatly limit its superiority, for example, it is sensitive to the parameter setting because of its definition based on the exponential operation, on the other hand, the Gaussian kernel needs costly computational time. Besides, the hidden information such as the distance information of the samples is conducive to improving the performance of face recognition. To overcome the above problems, we propose a reciprocal kernel-based weighted collaborative-competitive representation for face recognition. Different from other methods, a new reciprocal kernel is designed to realize the nonlinear representation of the samples. Moreover, a new weight based on the reciprocal kernel is imposed on coding coefficients to disclose the hidden information of the samples in the nonlinear space. With the help of the collaborative-competitive method, the proposed method can well achieve the trade-off between collaborative and competitive representation to promote the performance of face recognition. These factors explicitly encourage the proposed method to be a better representation-type classifier. Finally, extensive experiments are conducted on five benchmark datasets, and the experimental results show that the proposed approach outperforms many state-of-the-art approaches.