Distance Preserving Embeddings for General n-Dimensional Manifolds.

Abstract

Low dimensional embeddings of manifold data have gained popularity in the last decade. However, a systematic finite sample analysis of manifold embedding algorithms largely eludes researchers. Here we present two algorithms that embed a general n-dimensional manifold intoR d (where d only depends on some key manifold properties such as its intrinsic dimension, volume and curvature) that guarantee to approximately preserve all interpoint geodesic distances.