Shape dimension and approximation from samples
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth annual symposium on Computational geometry
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Random projection trees and low dimensional manifolds
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tighter bounds for random projections of manifolds
Proceedings of the twenty-fourth annual symposium on Computational geometry
Random Projections of Smooth Manifolds
Foundations of Computational Mathematics
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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 embed a general n-dimensionalmanifold into Rd (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.