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Low-rank representation (LRR) has aroused much attention in the community of data mining. However, it has the following twoproblems which greatly limit its applications:(1) it cannot discover the intrinsic structure of data owing to the neglect of the local structure of data;(2) the obtained graph is not the optimal graph for clustering. To solve the above problems and improve the clustering performance, we propose a novel graph learning method named low-rank representation with adaptive graph regularization (LRR_AGR) in this paper. Firstly, a distance regularization term and a non-negative constraint are jointly integrated into the framework of LRR, which enables the method to simultaneously exploit the global and local information of data for graph learning. Secondly, a novel rank constraint is further introduced to the model, which encourages the learned graph to have very clear clustering structures, ie, exactly c …