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

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.


Published in:
Proc. IEEE ICIP 2008
Presented at:
IEEE International Conference on Image Processing, San Diego, October 2008
Year:
2008
Keywords:
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 Record created 2008-01-21, last modified 2018-03-18

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