On a Connection Between Maximum Variance Unfolding, Shortest Path Problems and IsoMap
Abstract
We present an equivalent formulation of the Maximum Variance Unfolding (MVU) problem in terms of distance matrices. This yields a novel interpretation of the MVU problem as a regularized version of the shortest path problem on a graph. This interpretation enables us to establish an asymptotic convergence result for the case that the underlying data are drawn from a Riemannian manifold which is isometric to a convex subset of Euclidean space.
Cite
Text
Paprotny and Garcke. "On a Connection Between Maximum Variance Unfolding, Shortest Path Problems and IsoMap." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.Markdown
[Paprotny and Garcke. "On a Connection Between Maximum Variance Unfolding, Shortest Path Problems and IsoMap." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.](https://mlanthology.org/aistats/2012/paprotny2012aistats-connection/)BibTeX
@inproceedings{paprotny2012aistats-connection,
title = {{On a Connection Between Maximum Variance Unfolding, Shortest Path Problems and IsoMap}},
author = {Paprotny, Alexander and Garcke, Jochen},
booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics},
year = {2012},
pages = {859-867},
volume = {22},
url = {https://mlanthology.org/aistats/2012/paprotny2012aistats-connection/}
}