Distance Preserving Embeddings for General n-Dimensional Manifolds
Nakul Verma JMLR W&CP 23: 32.1 - 32.28, 2012
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, given access to just the samples, embed the underlying n- dimensional manifold into Rd (where d only depends on some key manifold properties such as its intrinsic dimension, volume and curvature) and guarantee to approximately preserve all interpoint geodesic distances.