Distance Preserving Embeddings for General n-Dimensional Manifolds

Nakul Verma
Proceedings of the 25th Annual Conference on Learning Theory, PMLR 23:32.1-32.28, 2012.

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 this Paper

BibTeX
@InProceedings{pmlr-v23-verma12, title = {Distance Preserving Embeddings for General $n$-Dimensional Manifolds}, author = {Verma, Nakul}, booktitle = {Proceedings of the 25th Annual Conference on Learning Theory}, pages = {32.1--32.28}, year = {2012}, editor = {Mannor, Shie and Srebro, Nathan and Williamson, Robert C.}, volume = {23}, series = {Proceedings of Machine Learning Research}, address = {Edinburgh, Scotland}, month = {25--27 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v23/verma12/verma12.pdf}, url = {https://proceedings.mlr.press/v23/verma12.html}, 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.} }
Endnote
%0 Conference Paper %T Distance Preserving Embeddings for General n-Dimensional Manifolds %A Nakul Verma %B Proceedings of the 25th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2012 %E Shie Mannor %E Nathan Srebro %E Robert C. Williamson %F pmlr-v23-verma12 %I PMLR %P 32.1--32.28 %U https://proceedings.mlr.press/v23/verma12.html %V 23 %X 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.
RIS
TY - CPAPER TI - Distance Preserving Embeddings for General n-Dimensional Manifolds AU - Nakul Verma BT - Proceedings of the 25th Annual Conference on Learning Theory DA - 2012/06/16 ED - Shie Mannor ED - Nathan Srebro ED - Robert C. Williamson ID - pmlr-v23-verma12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 23 SP - 32.1 EP - 32.28 L1 - http://proceedings.mlr.press/v23/verma12/verma12.pdf UR - https://proceedings.mlr.press/v23/verma12.html AB - 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. ER -
APA
Verma, N.. (2012). Distance Preserving Embeddings for General n-Dimensional Manifolds. Proceedings of the 25th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 23:32.1-32.28 Available from https://proceedings.mlr.press/v23/verma12.html.

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