A new manifold reconstruction method based on Isomap

Most of the existing nonlinear dimensionality reduction methods only realize data embedding from high-dimensional to low-dimensional data spaces but not data mapping between them, which restrict their applications to approximation and prediction tasks. This paper proposes two new data mapping methods, fast method and robust method respectively, which realizes data mapping from data embedding based on the intrinsic executive mechanism of Isomap, one of the most well known nonlinear dimensionality reduction method. It also presents theoretical estimations for the approximation precision and computational complexity of the new methods. Some experiment results on synthetic and real-world data sets are demonstrated, which verifies the feasibility and effectiveness of the new data mapping methods. Particularly, the simulations, which apply the new methods on feature movie description problem and pattern classification problem, are designed. The results further shows the potential usefulness of the new methods.