Together with the curse of dimensionality, nonlinear dependencies in large data sets persist as major challenges in data mining tasks. A reliable way to accurately preserve nonlinear structure is to compute geodesic distances between data points. Manifold learning methods, such as Isomap, aim to preserve geodesic distances in a Riemannian manifold. However, as manifold learning algorithms operate on the ambient dimensionality of the data, the essential step of geodesic distance computation is sensitive to high-dimensional noise. Therefore, a direct application of these algorithms to high-dimensional, noisy data often yields unsatisfactory results and does not accurately capture nonlinear structure.