A Version of Isomap with Explicit Mapping

Recently several manifold learning algorithms have been presented for nonlinear dimensionality reduction. Isomap is one of them. However, Isomap suffers from a deficiency that it does not give an explicit mapping function, which is from high dimensional space to low dimensional target space. In this paper, a version of Isomap with explicit mapping, called E-Isomap, is proposed. In E-Isomap, the geodesic distance matrix is fed into a cost function and then iterative majorization is adopted to solve an optimization problem for obtaining both the low dimensional configuration and the nonlinear mapping. Owing to the existence of explicit mapping, this version of Isomap can be more easily used in pattern recognition than the original ones. The experiments on two benchmark data sets are given to demonstrate the performance of the presented method