Distance Preserving Embeddings for General n-Dimensional Manifolds
Nakul Verma; 14(38):2415−2448, 2013.
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.
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