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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.
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