In practical data classification and data mining, on one hand labeled data is required to agglomerate knowledge;on the other hand it may be too expensive to be obtained. Inspired by this dilemma, this paper introduced a scheme of local approximations based semi-supervised manifold learning. This method is a combination of the classical semi-supervised learning and the manifold learning, thus inherits their advantages in overcoming the dilemma by using a large number additional unlabeled data with labeled data and in dealing with complex high-dimensional data by using manifolds, respectively. F...