中文说明：在许多实际应用中，数据更可能是在低维的
English Description：
In many real applications, the data is more likely to reside on a low dimensional submanifold embedded in the high dimensional ambient space. It has been shown that the geometrical information of the data is important for discrimination. In this paper, we propose a graph based algorithm, called Graph regularized Sparse Coding (GraphSC), to learn the sparse representations that explicitly take into account the local manifold structure of the data. By using graph Laplacian as a smooth operator, the obtained sparse representations vary smoothly along the geodesics of the data manifold. The extensive experimental results on image classification and clustering have demonstrated the effectiveness of our proposed algorithm.