Several different algorithms have been developed to perform dimension reduction of low-dimensional nonlinear manifolds embedded in a high dimensional space. For example, Isomap[8] was originally proposed as a generalization of multi-dimensional scaling. An alternative method known as locally linear embedding (LLE)[4]was developed that solved a consecutive pair of linear least square optimizations. More recently, another method for dimensionality reduction of manifolds has been described in terms of the spectral decomposition of graph Laplacians[9]. Although all three algorithms, Isomap, graph Laplacian eigenmaps, and LLE have quite different motivations and derivations, they all can perform dimensionality reduction on nonlinear manifolds. The author got the inspiration from these pioneering work and then made some improvements[4-5], it opened up new directions in nonlinear manifold learning, although many fundamental problems were required to be further investigated.