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conference paper
On the estimation of geodesic paths on sampled manifolds under random projections
2008
2008 15th IEEE International Conference on Image Processing
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.
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Mahmoudi4.pdf
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