Adaptive neighborhood selection for manifold learning

As a class of nonlinear dimensionality reduction methods, manifold learning can effectively construct nonlinear low dimensional manifolds from sampled data points embedded in high dimensional spaces. However, the results of most manifold learning algorithms are extremely sensitive to the parameters which control the selection of neighbors at each point. In this paper, an adaptive neighborhood selection method was proposed. Through ranking on manifold to select candidate neighborhood, and then estimating local tangent space, we can select the neighborhood of each point adaptively. Experimental results on several synthetic and real datasets demonstrate the effectiveness of our method.