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Local descriptor based image representation is widely used in biometrics and has achieved promising results. We usually extract the most distinctive local descriptors for image sparse representation due to the large feature space and the redundancy among local descriptors. In this paper, we describe the local descriptor based image representation via a graph model, in which each node is a local descriptor (we call it "atom") and the edges denote the relationship between atoms. Based on this model, a hierarchical structure is constructed to select the most distinctive local descriptors. Two-layer structure is adopted in our work, including local selection and global selection. In the first layer, L1/Lq regularized least square regression is adopted to reduce the redundancy of local descriptors in local regions. In the second layer, AdaBoost learning is performed for local descriptor selection based on the results of the first layer. We apply this method to long-range personal identification by using binocular regions. Our method can select the distinctive local descriptors and reduce the redundancy among them, and achieve encouraging results on the collected binocular database and CASIA-Iris-Distance. Particularly, our method is about 50 times faster than the traditional AdaBoost learning based method in the experiments.