On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap

Alexander Paprotny, Jochen Garcke
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:859-867, 2012.

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 this Paper

BibTeX
@InProceedings{pmlr-v22-paprotny12, 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}, pages = {859--867}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/paprotny12/paprotny12.pdf}, url = {https://proceedings.mlr.press/v22/paprotny12.html}, 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.} }
Endnote
%0 Conference Paper %T On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap %A Alexander Paprotny %A Jochen Garcke %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-paprotny12 %I PMLR %P 859--867 %U https://proceedings.mlr.press/v22/paprotny12.html %V 22 %X 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.
RIS
TY - CPAPER TI - On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap AU - Alexander Paprotny AU - Jochen Garcke BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-paprotny12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 859 EP - 867 L1 - http://proceedings.mlr.press/v22/paprotny12/paprotny12.pdf UR - https://proceedings.mlr.press/v22/paprotny12.html AB - 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. ER -
APA
Paprotny, A. & Garcke, J.. (2012). On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:859-867 Available from https://proceedings.mlr.press/v22/paprotny12.html.

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