Manifold learning with local geometry preserving and global affine transformation

This paper proposes a new approach to learn the low dimensional manifold from high dimensional data space. The proposed approach deals with two problems in the previous algorithms. The first problem is local manifold distortion caused by the cost averaging of the global cost optimization during the manifold learning. The second problem results from the unit variance constraint generally used in those spectral embedding methods where global metric information is lost. The formulation of the proposed method is described in details. Experiments on both low dimensional data and real image data are performed to illustrate the theory.