LRR is a popular technique for learning an efficient representation of image information and is reported to have excellent performance in machine learning and computer vision.However,LRR is an unsupervised method and has poor applicability and performance in real scenarios because of lack of image information.In this paper,we propose a novel semi-supervised approach for studying the lowest-rank representation among all the coefficient matrices that represent the images as linear combinations of the basis in the given dictionary,called semi-supervised Low-Rank Representation (semi-LRR),which incorporates the label information as an additional hard constraint.Specifically,we develop an optimization process in which the improvement of the discriminating power of the low rank decomposition is presented explicitly by adding the label information constraint.A semi-LRR graph is constructed to represent data structures for semi-supervised learning and the weights of edges in the graph is provided by seeking a low-rank and sparse matrix.The experimental results show the effectiveness of semi-LRR in comparison to the state-of-the-art approaches.