Distance Preserving Embeddings for General n-Dimensional Manifolds

Nakul Verma.

Year: 2013, Volume: 14, Issue: 38, Pages: 2415−2448


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 into $\R^d$ (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.