Distance Preserving Embeddings for General N-Dimensional Manifolds
Abstract
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 R^d (where d only depends on some key manifold properties such as its intrinsic dimension, volume and curvature) and \emphguarantee to approximately preserve all interpoint geodesic distances.
Cite
Text
Verma. "Distance Preserving Embeddings for General N-Dimensional Manifolds." Proceedings of the 25th Annual Conference on Learning Theory, 2012.Markdown
[Verma. "Distance Preserving Embeddings for General N-Dimensional Manifolds." Proceedings of the 25th Annual Conference on Learning Theory, 2012.](https://mlanthology.org/colt/2012/verma2012colt-distance/)BibTeX
@inproceedings{verma2012colt-distance,
title = {{Distance Preserving Embeddings for General N-Dimensional Manifolds}},
author = {Verma, Nakul},
booktitle = {Proceedings of the 25th Annual Conference on Learning Theory},
year = {2012},
pages = {32.1-32.28},
volume = {23},
url = {https://mlanthology.org/colt/2012/verma2012colt-distance/}
}