Data correspondences and data matching are important tasks of high-dimensional data analysis. In this paper, we discuss a family of semi-supervised learning algorithms for studying different manifold data sets corresponding. The algorithm improves local embedding or density models by elevating their status to full global dimensionality reduction without requiring any modification to their training procedures or cost functions. By using self correspondence between examples in the same data set, the method can improve the performance of these data sets with limited numbers of examples. The effec...