A two-step framework for highly nonlinear data unfolding

Local structures and global structures of data sets are both important information for learning from highly nonlinear data. However, existing manifold learning algorithms either neglect one of them or have limitation on describing them. In this paper, we proposed a new two-step framework that fusing the global and local information to unfold highly nonlinear data. It first learns the global structures via a new method—Distance Penalization Embedding and then refines the local structures by semi-supervised manifold learning algorithms. The effectiveness of the method has been verified by experimental results on both simulation and real world data sets.