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 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.
Cite
Text
Verma. "Distance Preserving Embeddings for General N-Dimensional Manifolds." Journal of Machine Learning Research, 2013.Markdown
[Verma. "Distance Preserving Embeddings for General N-Dimensional Manifolds." Journal of Machine Learning Research, 2013.](https://mlanthology.org/jmlr/2013/verma2013jmlr-distance/)BibTeX
@article{verma2013jmlr-distance,
title = {{Distance Preserving Embeddings for General N-Dimensional Manifolds}},
author = {Verma, Nakul},
journal = {Journal of Machine Learning Research},
year = {2013},
pages = {2415-2448},
volume = {14},
url = {https://mlanthology.org/jmlr/2013/verma2013jmlr-distance/}
}