Publication

On the estimation of geodesic paths on sampled manifolds under random projections

Pierre Vandergheynst, Matteo Sorci
2008
Conference Papers

Abstract

In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in high-dimensional Euclidean spaces. We show that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved by Gaussian projections and we characterize the distribution of geodesic lengths in the reduced dimensional point cloud. A stylized application to a real-world data set of human faces is presented to validate our theoretical findings.

Official source

https://infoscience.epfl.ch/entities/publication/78938c86-dfd7-494f-b57a-aa71a1abb528

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On the estimation of geodesic paths on sampled manifolds under random projections

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