Low-rank representation with adaptive graph regularization.

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, i.e., exactly c connected components for the data with c clusters. These two approaches are meaningful and beneficial to learn the optimal graph that discovers the intrinsic structure of data. Finally, an efficient iterative algorithm is provided to optimize the model. Experimental results on synthetic and real datasets show that the proposed method can significantly improve the clustering performance.